Rebound effects of power enhancement in internal combustion and electric vehicles

Abstract

Regulations and public expectations are compelling the road transport sector to innovate for higher vehicle efficiency. However, a persistent gap remains between official figures and real-world energy performance. This discrepancy is often linked to idealized testing environments and behavioral “rebound effects,” where improved efficiency leads to increased travel. This study introduces the “power rebound effect,” a new premise where increased horsepower impedes the deployment of efficiency gains. Analyzing a database of 531 car models from 15 years of real-world European testing, our findings reveal a significant power rebound effect in petrol and diesel cars, though not in electric ones. Additionally, rising vehicle weight induces a rebound effect across all vehicle types. This research provides a fuller understanding of the factors shaping passenger car fuel intensity, offering crucial insights for future energy policy.

Introduction

Transport-related emissions exhibited an annual growth rate of 1.7% from 1990 to 2022, surpassing the increase in any other end-use sectors except for industry (which also expanded at approximately 1.7%)^1–6. In 2022, the recovery of passenger and cargo transport activities post-COVID-19 pandemic resulted in a 3% upturn in CO₂ emissions from transport compared to the preceding year⁷. To align with the Net Zero Emissions by 2050 Scenario, there is a requisite for an annual reduction in CO₂ emissions from the transport sector exceeding 3% by 2030^8–11. Achieving these emission reductions will necessitate robust regulations, fiscal incentives, and substantial investments in infrastructure to facilitate the operation of low- and zero-emission vehicles. Around 45% of transport emissions come from passenger travel, mostly by means of personal cars, which makes this the most significant contributor in the sector overall. These emissions have increased by 79% since 1990 (World Resources Institute, 2021). Reducing the demand for energy in the transport sector is important to achieve current climate goals¹².

The trends in road passenger transport have a multifaceted impact on Europe’s CO₂ emissions¹³. A key measure to improve efficiency—and therefore reduce the emissions—of cars is by setting fuel intensity and carbon emission standards. Over the past 30 years, in which emissions have nearly doubled, cars have also become more efficient because of various innovations. Not only has the engine itself been improved, but more advanced technology like automatic transmission, better aerodynamics, lower N/V ratios, and start-stop systems has also decreased the overall fuel consumption of a car (The N/V ratio is the number of revolutions per minute of the engine, divided by the velocity of the vehicle, in top gear). Besides these innovations in cars with an internal combustion engine (ICE), completely new drivetrains have been developed. Hybrid electric vehicles cause large reductions in emissions at the tailpipe, and fully electric vehicles can be charged in alignment with renewable electricity generation to emit no carbon dioxide at all^14–16. With these fuel intensity improvements in passenger cars, one would expect the total global emissions coming from these cars to decrease, yet it has increased. Data shows that global CO₂ emissions from passenger cars have increased from 2.2 to 3.2 gigatons over the last two decades (Statista, 2022). In Europe, CO₂ emissions from the transport sector increased by 25% from 1990 to 2016 (European Parliament, 2019)^17,18.

A possible explanation for this counterintuitive phenomenon is the discrepancy between emissions measured under official test procedures and those observed in real-world driving. For many years, manufacturers relied on the New European Driving Cycle (NEDC) to determine fuel consumption and emissions. This test, introduced in 1970 and last updated in 1997, has been widely criticized for not adequately capturing typical driving conditions. Several studies have shown that the NEDC systematically underestimates fuel use and emissions compared to real-world driving patterns^19,20.

A study showed that the emissions gap in the Netherlands has significantly increased. By comparing data from car manufacturers with user data from company fuel passes (fuel records), the study found that this difference increased from 10% to 50% between 2004 and 2013²¹. On average, car models from 2013 and 2014 emitted 32% more on the road than during the NEDC test procedure. Similar and increasing differences have been observed across Europe²². In a different study, the same authors provided a summary of several reports, showing that this growing discrepancy exists not only in the Netherlands but also in Germany, Spain, and the United Kingdom²³. Due to this discrepancy, the Worldwide Harmonized Light Vehicles Test Procedure (WLTP) was introduced in September 2017. The earlier study investigated the potential impact of switching to the WLTP and based on simulations, predicted that although the WLTP would narrow the discrepancy, a 10–15% gap would remain²².

Another possible cause of this is the fact that there are more cars on the road. In emerging economies such as China and Eastern European countries, this is partly because cars have become more affordable, as wages have increased faster than the cost of vehicles (though in some Western European countries, such as Germany, the price of cars has increased above the wage rate, yet there are still more cars on the road). The number of registered passenger cars in the EU grew significantly from approximately 156 million in 1990 to nearly 247 million in 2020, reflecting a substantial increase in vehicle ownership over 30 years²⁴. This has substantially increased emissions, despite the improvements in efficiency. This is, in part, a modern example of a phenomenon first described by William Stanley Jevons in 1865 in his book The Coal Question. He noticed a similar effect in the use of coal-powered steam engines in the industrial era in Great Britain. As steam engines became more efficient, it became more affordable to use them for all kinds of new applications. This resulted in a larger total energy use than before²⁵—a phenomenon now known as the Jevons paradox. More recently, regarding cars, it has been found that the relationship between per capita car ownership and GDP is not straightforwardly linear. Initially, at lower GDP levels, the growth in the number of vehicles per capita tends to be gradual²⁶. However, this trend shifts dramatically with a significant upsurge, approximately doubling, when GDP per capita ranges from $3000 to $13,000. This trend is most likely associated to some extent with the phenomenon that became known as the rebound effect or the Jevons Paradox. A more general description of the rebound effect is that the expected energy savings of a newly introduced energy efficiency improvement for a certain product or service are (partially) offset because of an increase in use²⁷.

The power rebound effect, as we define it below, is different from the Jevons Paradox but may add a new implication to it. It leads us to ask: Is part of the increase in energy consumption (or the failure to reduce energy consumption by the technically expected amount) a consequence of the increase in vehicle engine power? If so, how large is this rebound effect? While many articles consider the rebound effect to be caused by energy efficiency rather than other properties of a car, this paper looks for evidence of a specific type of rebound effect in the European car market, namely the power rebound effect.

Investigating the power rebound effect is important because increased vehicle power affects driving style, making it easier for drivers to accelerate and to travel uphill at high speeds, thereby consuming more fuel. These driving practices become habitual, locking this extra fuel consumption into the regular pattern of driving practice.

Note that there are a number of different technical features or upgrades that lead to increases in vehicle power, such as an increased number of engine cylinders, larger cylinders, more generous fuel injection, and higher compression ratios. This paper is not concerned to investigate these, but instead to map the association between increases in vehicle power and increases in fuel consumption.

Despite decades of technological improvements in powertrains, aerodynamics, and regulatory fuel-economy targets, the real-world fuel intensity of passenger vehicles has not fallen in line with laboratory ratings. The European Commission’s first report based on on-board fuel-consumption monitoring of 2022 registrations shows that real-world CO₂ emissions and fuel use are on average about 20% higher than official WLTP values (First Commission report on real-world CO₂ emissions of cars and vans using data from on-board fuel consumption monitoring devices—Climate Action, 2024). Independent analysis by the International Council on Clean Transportation confirms a persistent and growing gap between type-approval and on-road fuel consumption for European cars through 2022²⁸. Beyond measurement gaps, improved efficiency lowers the per-kilometer cost of driving and thereby induces additional travel—an example of the rebound effect, mentioned above, here defined as the energy efficiency elasticity of distance traveled, or more generally of energy consumption. Recent syntheses report short-run rebound elasticities of roughly 10–30% and long-run elasticities approaching 30–50%, implying that a sizeable share of engineering fuel savings is offset by behavioral responses^29,30.

Recognizing this “rebound” perspective allows policymakers to methodologically integrate these feedbacks when evaluating efficiency policies: by estimating demand elasticities for vehicle travel, explicitly modeling fleet turnover and consumer choice, and complementing efficiency standards with carbon pricing, distance-based charges, or feebate schemes, they can better predict and secure the real reductions in fuel consumption and greenhouse-gas emissions.

Section “Literature review” introduces the background and the theory behind this topic. Section “Results” shows the results of this research. Section “Discussion” discusses the possible shortcomings of this research. Section “Conclusions” provides the conclusions. Section “Methods” provides the dataset and summarizes the methodology for how this research is performed.

Literature review

This section takes a more comprehensive look at the rebound effect: how the effect can be quantified, the different types of rebound effects³¹, and how the research reflected in this paper takes a different approach.

The rebound effect, an “umbrella term”

The widely accepted economic view on the rebound effect stems from the research done in 1980^15,32. Despite not naming the term “rebound effect”, Khazzoom describes it as a phenomenon in which an efficiency increase, or a cost reduction due to efficiency, leads to increased use of a product or service because of behavioral responses or systemic effects, and which, therefore, at least partly counteracts the pure efficiency effect^33,34. Traditionally, the rebound effect is defined to be direct, indirect, or economy-wide^31,35:

1. A direct rebound effect means that there is a rebound acting on the product itself, a car in this case. An example of this would be the distance rebound effect, a phenomenon where the use of a more efficient car results in a larger distance driven.

2. Indirect rebound effects take effect in a different place from where the energy efficiency change is made. For instance, the fuel intensity of a car improves, and a consumer saves money on driving, but the money saved can be spent on an airplane ticket for an overseas holiday.

3. Economy-wide effects refer to the sum of the direct and indirect rebound effects, as well as any rebound from an energy efficiency improvement, inducing changes in the use of energy to produce complementary and substitute goods and other flow-on effects that affect energy use across the economy.

This classification of the rebound effect probably bears its origins in the domain of economics, as exemplified by its similarities with some theoretical tools of marginalism (i.e., Slutsky equations for substitution and income effects). Indeed, there is no trace of such a classification in other fields of science that are theoretically or empirically related to energy efficiency enhancement and energy use, for example, as in Finite-Time Thermodynamics or the Minimum/Maximum Entropy Production dilemma^36,37.

However, there is a growing consensus among scholars that rebound effects cannot be restricted to these three types (and related metrics), and “rebound effect” should be rather considered an “umbrella term” encompassing any kind of systemic energy-use response to an energy efficiency change, such as time-rebound effects (when a time-saving technology leads to more energy intensive usage) or frontier-rebound effects (when a more efficient process enables the production of an altogether new artifact)³⁸. Below, we illustrate three types of rebound effects inherent to the transport sector.

Distance rebound

The distance rebound effect, or fuel intensity rebound effect, describes the phenomenon where a greater distance is traveled because the fuel intensity of a vehicle is improved³⁹. At constant energy prices, the relative cost of traveling comes down; hence, one can travel further with the same monetary budget⁴⁰. This ultimately results in more energy being used than the energy that was theoretically expected to be used due to the better fuel intensity. In theory, a car that is twice as energy efficient would consume half as much fuel on that journey. However, since that also means half the fuel cost of the journey, drivers can now choose to drive further to more places with a similar budget. The increase in traveled distance rebounds on the intended fuel use.

The distance rebound effect is generally easy to measure. Therefore, a lot of research has already been done on this topic. Most of it is in the United States, where estimated rebound effects ranging from 5 to 25% were found⁴¹. However, more recent studies have found that the distance rebound effect could range from 20 to 40%⁴⁰. In Europe, various studies have shown that the distance rebound effect is larger than in the US. In Great Britain, the effect ranges from 9 to 36%, with an average of 19%⁴². Another study found a rebound effect ranging from 57 to 62% in Germany⁴³. More recently, with a larger and updated dataset, the distance rebound effect in Germany was found to be 58%, which is similar to 60% found in Switzerland^44–46. In China, studies have shown that the distance rebound effect for passenger cars is as high as 96%, nearly canceling out the efficiency improvements^47–49. Other factors, such as total annual driving distance, the education level of car owners, and the energy source of the vehicle (petrol, electricity, etc.), were found to further influence this phenomenon^15,50. Additionally, some of these factors were found to be interrelated⁵¹.

Speed rebound

The speed rebound effect suggests that some of the shortfall in fuel saving is not coming from the traveled distance but rather from an average speed increase. More fuel is utilized when driving at higher speeds per distance traveled. When a car is more fuel-efficient, it becomes more affordable to drive faster. Therefore, driving faster and thus reaching a destination faster becomes more economically viable, assuming the cost of energy remains constant.

The speed metric is arguably more difficult to measure because, besides the traveled distance, the time component is needed. Time data for specific journeys are not easy to collect, especially in passenger vehicles. However, research used data from two seasons of Formula 1 pre-race time trials, when there were minimal technical engine regulation changes, to show the presence of the speed rebound effect. The data from testing sessions were used, so there were no competitors who could influence the drivers’ performance⁵². This sport provides extremely accurate measurements, and it shows that the energy efficiency improvements were completely countered by the increases in speed. There was a 100% speed rebound effect in these racing cars. It is expected that a rebound of this type would also occur in passenger vehicles.

Power rebound

Contrary to the distance and speed rebound effect, the power rebound effect suggests that the (rated) power of the engine, rather than energy efficiency, is a cause of rebound. A study suggests that the fuel intensity of passenger cars from 1980 to 2006 would be almost 60% higher if the weight, horsepower, and torque were held at the 1980 levels⁵³. In theory, a more powerful engine of the same size should be more efficient because, in Otto or Diesel cycles, first-order efficiency is proportional to the compression ratio⁵⁴. However, more available power can result in more aggressive driving behaviors. Drivers of more powerful cars may be more likely to engage in harsh maneuvers such as fast acceleration, quicker cornering, or harder braking. The impact of these driving behaviors on fuel efficiency is difficult to measure reliably, and there has been limited investigation into this topic. Recently, focusing on the power rebound effect in freight trucks⁵⁵, an innovative method was used to bypass the behavior-related part of the power rebound effect. The research concluded that there is a rebound effect of 18% due to the increase in engine power of the studied freight trucks.

The rebound effect can therefore have many sources, not only from technological improvements that are expected to reduce the energy use of a car^15,56–59. Another source of rebound can be the power of an engine. To build on the concept of the rebound effect having many sources, our research applies a similar approach to passenger cars with a wider scope.

Quantifying the rebound effect

Since the power rebound effect is based on the energy consumption of a car, the effect is defined as the proportionate change in energy intensity (also called “fuel intensity”) as a ratio of the proportionate change in power, i.e., the power elasticity of energy intensity. This can be expressed by Eq. (1), where $R$ is the rebound effect, $E$ is energy intensity, $\mathit{P}$ is average power, $\partial \mathit{E}$ is the average change in energy intensity, and $\partial P$ is the average change in power.

$$R=\frac{\partial E}{E}\left./\frac{\partial P}{P}\right)$$ 1

Note that this differs from the classic expression of the rebound effect⁶⁰:

$$R=\raisebox{1ex}{$\frac{\partial S}{S}$}\!\left/ \!\raisebox{-1ex}{$\frac{\partial \eta }{\eta }$}\right.$$ 2

where $S$ is energy services, such as distance traveled, or speed attained, and $\eta$ is energy efficiency. The power rebound effect may or may not be influenced by an energy efficiency increase, and the dynamic that we are interested in is how an increase in power itself leads to an increase in energy intensity.

Rebound effects calculated in Eq. (2) can have a variety of outcomes. Most often, a rebound effect is expected to be somewhere between zero and one, i.e., between 0 and 100%. A rebound effect of 1 (i.e., 100%) means that each 1% increase in power is associated with a 1% increase in energy services. However, a rebound effect does not have to be between 0% and 100%. For example, it has been found that the change in energy consumption when switching from traditional lightbulbs to certain LED and CFL lightbulbs was greater than expected, resulting in a “negative” rebound effect⁶¹. An overview of classic rebound effect outcomes is given in Table 1.

Table 1.

The possible outcomes of rebound effects

Realized efficiency	Rebound effect
Greater than expected efficiency	<0
Equal to expected efficiency	0
Less than expected efficiency	0–1
Zero	1
Worse than the previous efficiency level (backfire)	>1

The power rebound effect, as we define it in Eq. (1), has a similar range of dimensions, but its meaning is different. In Eq. (1), any value of R above zero means that more energy is being consumed. Therefore, the environmental effect is comparable to a classic rebound effect >1, i.e., higher than 100%, which has serious implications for vehicle emissions.

Technical improvements in vehicles are supposed to reduce climate emissions, and a classic rebound effect of <100% shows that they do so, but by less than the engineering calculations would predict. In contrast, the power rebound effect identifies a dimension where even this venture is failing. Energy intensity, and therefore energy consumption, is increasing rather than decreasing.

It is worth noting that the three different types of passenger vehicle rebound effect discussed above can be additive. A car-driver combination can exhibit a distance rebound effect (i.e., the driver travels further, as the increased energy efficiency makes this cheaper), a speed rebound effect (she travels faster, again because the increased energy efficiency makes this cheaper), and a power rebound effect (she accelerates more intensely because the increase in power makes this easier and more routine). Each of these rebounds will have a magnitude: for example, distance rebound 25%, speed rebound 20%, and power rebound 15%. Theoretically, they could be combined in one expression, namely:

$$R=\frac{\partial D}{D}\left./\frac{\partial \eta }{\eta }\right)+\frac{\partial V}{V}\left./\frac{\partial \eta }{\eta }\right)+\frac{\partial E}{E}\left./\frac{\partial P}{P}\right)$$ 3

where D is distance, V is speed, and the other variables are as given above. Note, however, that each expression is a partial differential and would therefore need to be estimated independently of the others to prevent double-counting, although this is routine in multivariate analyses. A further issue is that each expression is conceptually different, so adding them together would give only a rule-of-thumb indicator (60% in this example), not a measure of any particular parameter. A more numerically robust approach would be to convert each expression to its equivalent in excess annual fuel usage and simply add these up, although this would require a great deal of detail about specific drivers’ habits, journeys, etc., over a full year.

In this paper, we leave these questions aside for possible future research and simply focus on the power rebound.

Results

The regression results that enable power rebound effects to be estimated are given below for each fuel type and weight class.

Petrol-powered vehicles

The multivariate log-log regression for petrol cars (but using log-linear for the year of manufacture) shows that there is a statistically significant result for all five of the independent variables influencing the fuel intensity (Engine power, weight, aerodynamic constant, N/V ratio).

The rebound effect can be calculated from the data in Table 2 as explained in the section “Methods”. Using the coefficients from Table 2, this multiple-linear model can be expressed as:

$$\begin{array}{c}logF=199.463-0.0132Y+0.257logP\hfill \\ +0.56logW+0.432logC+0.21logN+\mathrm{er}\hfill \end{array}$$ 4

where $F$ = Fuel intensity [L/100 km], $Y$ = year, $P$ = rated engine power [hp], $W$ = weight [kg], $C$ = aerodynamic constant, and $N$ = N/V ratio, er = other influences not accounted for in the model.

Table 2.

Results of the multiple log-log (log-linear for year) regression for all petrol cars

Petrol cars	230 observations
Regressed against log fuel economy (L/100 km) tested by Quattroruote
		Coefficient	Standard deviation	t value	p value
Intercept		199.463	48.402	4.121	<0.001
Year		−0.013	0.003	−4.203	<0.001
Log_Engine power		0.257	0.027	9.243	<0.001
Log_Weight		0.560	0.102	5.492	<0.001
Log_C		0.432	0.096	4.511	<0.001
Log_N/V ratio		0.210	0.078	2.704	0.008

Residual standard error: 0.009223 on 112 degrees of freedom, 118 observations (112 observations deleted due to missing data), Multiple R-squared: 0.8552, Adjusted R-squared: 0.8487, F-statistic: 132.3 on 5 and 112 DF, p value: <2.2e-16.

The descriptive statistics of the sample reveal the evolution of mass and power across different powertrains (Diesel, Petrol, and Electric) over time. Diesel vehicles showed a gradual increase in both mass and power, with the average weight rising from 1688.5 kg in 2009 to 2064.5 kg in 2021, and the engine power increasing from 169.3 HP to 188.5 HP over the same period. Petrol vehicles exhibited a more significant increase, with the average weight growing from 1250.6 kg in 2009 to 1582.8 kg in 2018, and power surging from 136.4 HP to 288.3 HP by 2020. Electric vehicles, which have the highest average weight, saw an increase from 1402.3 kg in 2011 to 2066 kg in 2021, while their power grew from 155 HP to 324 HP during the same period. This evolution reflects the positive correlation between mass and power across all powertrains, with electric vehicles showing the most substantial increase due to advancements in battery technology.

The regression coefficient of Log_Engine power in Table 2 is 0.257. This indicates that each percentage increase in power is associated with an increase in fuel intensity of 0.257%—a power rebound effect of 25.7%. As shown by the formula in the power-year plot in Fig. 1, the average power of petrol engines has increased by 7.1 horsepower on average each year, which is an annual increase of 3.5% from its level in 2018. Meanwhile, the average energy intensity over this period has been 7.27 L/100 km, and the average horsepower has been 227.83 hp. A power rebound of 25.7%, therefore, indicates that each year, the increase in power is associated with an increase in fuel intensity of about 0.0318 L/100 km (holding all other influencing factors constant). Over the 15 years of the road tests, increases in power are, therefore, the likely cause of an increase in fuel intensity of 0.413 L/100 km, or 5.69%.

Fig. 1.

The power trends of three types of cars.

This might not sound very high, but it erodes the gains made through energy efficiency, drive train efficiency improvements (via reductions in N/V ratio), and reductions in aerodynamic drag coefficient. It also adds to the increases in fuel intensity due to increases in weight. As seen in Table 2, weight has an upward effect of 56.1%, while aerodynamic constant and N/V ratio have rebounds of 43.2% and 21.0%, respectively, since these two parameters are steadily enhancing. In this respect, the study shares similar findings to those of Galvin and colleagues^54,55. The variable “Year” acts as a proxy for other influences, such as increases in engine efficiency, that are not specifically identified in the database. The negative regression coefficients indicate that these factors are exerting downward pressure on fuel intensity. However, as shown in the bivariate plot in Fig. 1, fuel intensity has been increasing. This increase in fuel intensity suggests that the positive effects of increased power and weight have more than offset the downward pressure from reductions in aerodynamic constants, N/V ratio, and other unidentified influences such as improvements in energy efficiency. For a more detailed examination of the bivariate relationship between power and energy consumption, please refer to Figs. A1–A5 (in supplementary materials), which illustrate the relationship between fuel test data (fuel_test_right) and power (Power_hp) for different energy types.

In the database, there are 132 lightweight petrol cars (<1500 kg). Their observations were isolated from the database and analyzed using the same calculation method as above. The regression coefficients of engine power, weight, and the aerodynamic constant are statistically significant with p < 0.1. The complete table containing the results of the multiple log-log regression for each weight class is available in the supplementary document. Graphs that provide the yearly trends (e.g., Fig. 2) for the lightweight cars are also available in the supplementary document. The power rebound effect of lightweight petrol cars is 25.4%. The other rebound effects are listed in Table 3.

Fig. 2.

A complete overview of all trends in the complete dataset from the Quattroruote magazines.

Table 3.

All statistically significant rebound effects in different types of petrol-engine cars

	Petrol general	Petrol light	Petrol medium	Petrol heavy
Power	25.70%	25.40%	27.00%	-
Aerodynamic constant	43.20%	-	65.40%	-
N/V ratio	21.00%	28.30%	-	-
Control variable
Weight	56.00%	47.60%	-	-

There are 81 mediumweight petrol cars (1500–2000 kg) in the database. They did not show significance for every variable. The N/V ratio has a p value of 0.1931. Therefore, the rebound effect from this property is not included in the results. The power rebound effect of this type of petrol car is 27.0%. There are only 17 heavyweight petrol cars (>2000 kg) in the database. Since n ≥ 30 is ideally required for multiple log-log regression to be significant, there are no results from this type of car.

Diesel

The same methods were applied to diesel cars. First, the multiple log-log (similarly, log-linear for Year) regression results of all 230 diesel-powered cars in the database are shown in Table 4. The regression shows statistical significance for all five independent variables. Similar to the subsection on petrol-powered cars, diesel-powered cars are divided into different weight groups to see if rebound effects are more pronounced for certain types of cars. A complete overview of all rebound effects in different weight classes of these cars is given in Table 5.

Table 4.

The result of the multiple log-log regression for all diesel cars

Diesel cars	230 observations
Regressed against log fuel economy (L/100 km) tested by Quattroruote
	Coefficient	Standard deviation		t value	p value
Intercept	326.064	32.728		9.963	<0.001
Year	−0.0216	0.002		−10.142	<0.001
Log_Engine power	0.082	0.043		1.923	0.056
Log_Weight	0.962	0.077		12.501	<0.001
Log_C	0.325	0.066		4.901	<0.001
Log_N/V ratio	0.225	0.061		3.697	<0.001

Residual standard error: 0.07411 on 152 degrees of freedom (72 observations deleted due to missingness), Multiple R-squared: 0.8546, Adjusted R-squared: 0.8499, F-statistic: 178.7 on 5 and 152 DF, p value: <2.2e-16.

Table 5.

All statistically significant rebound effects in different types of diesel cars

	Diesel general	Diesel light	Diesel medium	Diesel heavy
Power	-	-	-	-
Aerodynamic constant	32.50%	-	33.5%	32.3%
N/V ratio	22.5%	-	17.7%	-
Control variable
Weight	96.2%	-	109.1%	107.7%

There are 46 lightweight diesel-powered cars in the database. The regression showed that none of the properties has statistical significance. The complete results are available in the supplementary document. There are 136 recorded mediumweight diesel-powered cars in the database. The weight, aerodynamic constant, and N/V ratio show statistical significance. The complete results are also available in the supplementary document. The multiple log-log regression on heavyweight diesel-powered cars showed statistical significance for weight and the aerodynamic constant. All the rebound effects that come from properties with a statistically significant impact on the fuel intensity are listed in Table 5.

To assess whether the correlation between engine power and vehicle weight affects the baseline estimates, we conducted an additional robustness check by mean-centering both log(power) and log(weight) and estimating models that include their interaction term. This allows us to evaluate whether the joint effect of power and weight materially alters the interpretation of our main specification.

For petrol vehicles, adding the centered interaction term leads to only minor changes in the coefficients of the main variables. The coefficient on log(power) changes from 0.257 in the baseline model to 0.244 in the interaction model, and the coefficient on log(weight) changes from 0.561 to 0.507, with both remaining highly significant (p < 0.001). The interaction term itself is statistically significant, but its inclusion results in only a marginal increase in model fit (adjusted R-squared from 0.849 to 0.861). These results indicate that the baseline model already captures the independent contributions of power and weight adequately (Table 6).

Table 6.

The result of the multiple log-log regression for all-electric cars

Electric cars	71 observations
Regressed log fuel intensity tested by Quattroruote
	Coefficient	Standard deviation	t value	p value
Intercept	−15.671	15.320	1.023	0.312
Year	−0.008	0.008	−1.102	0.276
Log_Engine power	0.072	0.064	1.133	0.263
Log_Weight	0.582	0.173	3.371	0.002
Log_C	0.259	0.208	1.243	0.220

Residual standard error: 0.1334 on 46 degrees of freedom (20 observations deleted due to missingness), Multiple R-squared: 0.6204, Adjusted R-squared: 0.5874, F-statistic: 18.8 on 4 and 46 DF, p value: 3.219e-09.

For diesel vehicles, the interaction term contributes nothing to the explanation of fuel consumption. The estimated interaction coefficient is essentially zero (0.005, p = 0.97), and the coefficients on log(power) (0.082) and log(weight) (0.963) remain almost identical to those in the baseline model. The adjusted R-squared also remains unchanged at 0.849, indicating no improvement in model performance. This finding is consistent with engineering considerations: diesel fuel consumption is driven primarily by vehicle weight due to high low-RPM torque, while horsepower plays a comparatively smaller role.

In both models, variance inflation factors remain comfortably below the conventional threshold of 10 (e.g., VIF < 6 for the main variables and <2 for the interaction terms), confirming that multicollinearity is not a concern. Overall, the robustness checks show that including an interaction term does not materially improve the explanatory power of the model, nor does it change the substantive conclusions. For this reason, we retain the more parsimonious specification without interaction terms in the main analysis.

Electric

There are 71 electric-powered cars recorded in the data. When dividing the 71 cars into different weight groups, none of the groups has n ≥ 30. Therefore, sub-grouping will not be made for electric-powered cars. Considering all-electric cars together, only the weight shows a statistically significant rebound effect, namely 58.20%. However, the lack of significance for the other variables might simply indicate that there is insufficient data on electric vehicles to produce reliable results for these. It does not necessarily mean that there is no speed rebound.

Discussion

This study investigated changes in average fuel intensity (L/100 km) associated with changes in the average power rating (horsepower) of cars. It found that for petrol cars, a 1% increase in power rating is associated with a 0.257% increase in fuel intensity. Taking into account current annual increases in power rating of 5.4 hp/year with an average power rating of 245 hp in 2024 (see Subfigure 2 in Fig. 2) and the average level of fuel intensity of 7.0 L/100 km in 2024 (see Subfigure 1 in Fig. 2), we calculated that this leads to an annual increase in fuel intensity of 0.0318 L/100 km. As we noted, these increases in fuel intensity erode the gains made by increased energy efficiency, reduced N/V ratio, and improved aerodynamic constant. We note that increases in vehicle weight also lead to increased fuel intensity, and this is a further cause of energy consumption being higher than it needs to be. A much smaller power rebound was found for diesel cars, and results for electric cars were indeterminate due to low statistical significance (high p values), possibly due to different inner mechanisms or the small number of observations.

The study fills a gap in rebound effect literature on cars, i.e., road vehicles weighing less than 3500 kg. As noted in the section “Literature review,” most such studies identify “distance” rebound effects, where drivers travel further due to cheaper journeying as energy efficiency increases. One study identifies speed rebound effects, but this is for Formula 1 racing cars, not passenger cars⁵². Another study focuses on rebounds due to weight increases, specifically with electric vehicles⁶². Attempts have also been made to integrate the effects of horsepower increases into rebound effect studies.

This study makes a unique contribution by focusing on the effects of power increases on fuel intensity and using the results of actual road tests by trained drivers in typical traffic conditions. This is important because drivers respond to what the engine offers them as they work their way through the stops, starts, slow crawls, and faster sections of a typical journey. We can hypothesize that extra engine power offers a driver many opportunities for faster acceleration and that the driver may take these opportunities without necessarily thinking about them. When the traffic lights turn green, or an opportunity to overtake a slow vehicle arises, a little extra pressure on the accelerator has big effects if the car has higher horsepower. A carefully designed study using both qualitative and quantitative methods would help identify such phenomena—the qualitative part would ask the drivers about their subjective experience of driving a more powerful car, and the quantitative part would map the acceleration patterns and other related variables.

The study also has various policy implications. First and foremost, the pursuit of zero carbon emissions will be hampered by continual increases in horsepower. This study showed its effect on petrol and diesel ICE cars, but the data were insufficient to confidently identify the effects among electric vehicles. The study is still highly relevant despite the transition to electric vehicles. Although most major car manufacturers are now focusing on vehicles with alternative drivetrains (“List of Production Battery Electric Vehicles”, 2022), approximately 90% of newly registered cars were still ICE-powered in 2021 (European Environment Agency, 2021). Despite the EU’s ban on the sale of new ICE cars post-2035 (European Union, 2019), a significant secondary market will persist, and ICE cars will likely remain in use for many years thereafter.

Therefore, the main implication for policy is the need to curb increases in vehicle power. It has been argued that there is a cultural celebration of increased horsepower in vehicle manufacture and advertising in the US⁶². An example is General Motors’ promotion of one of its most powerful sports utility vehicles: “Introducing the world’s first all-electric super truck, GMC HUMMER EV. With 1000 hp and 11,500 lb.-ft. of torque, it has the power and technology to conquer both on and off-road with extraordinary confidence.” Policies could disincentivize the continued increase in horsepower through steeply graded annual vehicle registration fees and higher sales taxes for more powerful vehicles.

Second, these would come alongside mitigation strategies for curbing rebound effects associated with increased distance and speed, such as stricter speed limits and road pricing based on travel distance. A technical policy example is the 2017 introduction of the WLTP, which reduced discrepancies in emissions testing results despite a continuing increase in average vehicle power. Nevertheless, a power rebound effect persists in petrol-engine cars, underscoring that the effect is not merely a byproduct of outdated testing procedures.

Regarding the method used in this study, some readers might find the term “rebound effect” inappropriate for mapping the effects of increases in horsepower. A “rebound effect” is traditionally taken to mean a failure to reduce energy consumption by the amount expected after a technology improvement (consumption did not go right down as far as expected but rebounded back upwards). However, this is merely a matter of terminology, not of method.

To enhance this type of research, expanding the dataset would provide more robust trend estimates. The current dataset has gaps, with some variables missing for certain cars, which slightly reduces the robustness of the multiple log-log regression model due to necessary omissions. Future studies could enrich the existing database or establish a new one, including for countries outside Europe, and perform analyses for additional car companies in a manner similar to that of Quattroruote.

Conclusions

Using a comprehensive database of 15 years of car tests performed by the Italian car magazine Quattroruote, this study used multivariate analyses with log-log transformations to estimate the relationships of a range of key variables with fuel intensity. These are the year of manufacture, horsepower, weight, aerodynamic drag constant, and N/V ratio. For petrol cars, it found all variables, except year of manufacture, positively correlated with fuel intensity. Of these, horsepower and weight have been steadily increasing, so these have put increasing upward pressure on fuel intensity. This dampens and even negates the downward pressure on fuel intensity that is being won by steadily reducing the aerodynamic drag constant and N/V ratio.

As noted above, the variable “year of manufacture” acted as a proxy for other influences, such as increases in engine efficiency, which were not specifically identified in the database. Its negative regression coefficient showed that these influences were putting downward pressure on fuel intensity, but fuel intensity kept increasing. This was because increases in power and weight have rather canceled downward pressures due to reductions in aerodynamic drag constant and N/V ratio. The study found these effects were largest for petrol cars and less so for diesel cars, while results for electric cars were indeterminate. The comprehensive exploration offers insights into the changing dynamics of passenger cars and their impact on fuel efficiency.

The study has also recommended a suite of policy measures that could help to reduce the horsepower of new vehicles. It would not seem feasible for policy to prevent new vehicles from being produced with increased horsepower, but the measures suggested would be designed to strongly disincentivize it. Interestingly, average horsepower reduced sharply, by 40%, in 1976–1982 during the period of the oil crisis. Clearly, there were social and cultural adaptations to driving lower-powered vehicles. However, horsepower then steadily increased to over twice its 1982 level by 2018⁶³, continually compromising gains made through increases in engine and drive train efficiency. Such high horsepower does not seem to be technically necessary for adequate journeying. Further studies could explore the cultural characteristics that help drive the predilection for ever-increasing horsepower. Meanwhile, policy needs to act decisively to disincentivize it.

While the study found that increases in vehicle power are associated with statistically significant increases in fuel intensity in petrol and diesel cars, it was not equipped to discover the mechanisms behind this. Presumably, this has to do with driver behavior: a response to increased power that may well be unconsciously exercised. Future research should investigate the multi-layer and causal relationships between variables such as weight, aerodynamic constant, N/V ratio, power, and fuel intensity. This inquiry would offer a comprehensive view of how these factors impact fuel consumption to quantify how power mediates the relationship between weight and fuel intensity. Additionally, it should clarify the dual role of weight, not only as a direct contributor to fuel intensity but also through its effect on power.

Moreover, although the present study does not integrate the recently released official real-world monitoring data due to its limited temporal overlap with our long-term sample⁶⁴, this source offers meaningful potential for future research. As the real-world database continues to accumulate more years of observations, it will provide increasing opportunities to compare controlled testing results with actual on-road performance for matched vehicle models. Future work may therefore explore harmonizing the two sources to examine systematic deviations between laboratory conditions and everyday driving behavior and to refine long-term trend estimates under real-world usage patterns.

Methods

This section explains the data methods to determine the rebound effect. Collecting data for the rebound effect in the car industry is not straightforward. There is limited government data on the real-world fuel consumption of passenger cars. Therefore, this study resorts to data made available in online public databases.

Cars are tested by Quattroruote (https://www.quattroruote.it/), a company that publishes reviews on cars in a reputable Italian car magazine that has provided detailed reports on European market introductions since 1956⁶⁵. These tests offer extensive data on various car variables, facilitating in-depth trend and correlation analyses. The cars are selected from a wide range, not just exotic models, which other magazines often focus on. All tests are performed at similar locations, and the tests are conducted by a select group of Quattroruote’s professional test drivers. These drivers operate the cars on a racetrack for performance testing and on public roads in urban, city, and highway settings. The racetrack tests mainly evaluate pure performance, while the road tests reflect real-world traffic conditions. During the road tests, the cars are equipped with multiple sensors to measure a variety of data points, such as fuel consumption, vehicle speed, engine load, and power output, as well as noise levels and vibrations during engine startup. The road tests are performed twice, with results deemed valid only if the average speed difference between the two tests is less than 2%. This consistency, combined with a controlled testing environment, ensures the reliability of the data and establishes a credible setup for analyzing the relationship between a car’s properties and its energy efficiency.

Yearly trends

The subgraphs shown in Fig. 2 are an overview of how the cars included in this dataset have developed over the years. Each dot represents one property of the cars that were recorded in the database. Not every property is applicable to each car, and not every property is published in the magazine each year. The outliers on some of these plots are removed. A trendline based on all observations in the plot is added. Figure 2 shows what these trends look like.

Some insights can be found from these trends. Although cars have become more powerful, the cylinder capacity stays at a similar level. This indicates that more power is being obtained from a similar-sized engine nowadays. The N/V ratio (bottom right) has decreased, meaning engines require less RPM to maintain a speed of 130 km/h when traveling in max gear. Cars have also become more aerodynamic, which has a positive effect on fuel economy since cars must overcome less drag resistance.

Two other trends that stand out are related to the fuel economy. The fuel economy measured during the Quattroruote tests is trending down by an average of −0.097 L/100 km per year, while the fuel economy specified by the manufacturer is moving upwards by 0.057 L/100 km per year. Again, this is likely the result of the introduction of the WLTP in 2017. Manufacturers have reported more realistic fuel economies ever since. Data shows that both manufacturers and the tests show a decrease in CO₂ emissions of −2.6 g/km per year and −6.4 g/km per year, respectively. Considering that the fuel use per 100 km in the road tests decreases over time, lower CO₂ emissions are expected. If less fuel is needed to cover a similar distance, fewer grams of CO₂ should be released into the air over that same distance. This does not seem to apply to the data from manufacturers, however. The data shows that the average fuel economy increases, but the CO₂ emissions per-kilometer come down. One final takeaway, the fuel economy from the tests is coming down despite the increase in power and weight, but the question remains whether the fuel economy would show a bigger downtrend if the power did not trend upwards as much as it does now.

Fuel consumption is measured using high-precision flowmeters that are regularly calibrated to ensure accurate readings during driving tests. The measurements are corrected for external temperature variations, ensuring consistency across tests. Emissions are measured using a Portable Emissions Measurement System, which records carbon dioxide, nitrous oxides, and particulate matter from the car’s exhaust. These measurements adhere to the WLTP standards introduced in 2017. To ensure data reliability, emissions testing is conducted under controlled environmental conditions, taking into account factors such as road type, driving style, and vehicle load.

The data varied from 2009 to 2023. Besides power and fuel consumption, a large number of other variables have also been collected to examine if they play a role in the rebound effect. The database consists of 531 car models and 23 observed variables. Some of the observed variables are used to calculate new metrics, but not every variable is applicable to each car. In total, the database consists of roughly 9000 entries. A list of the collected variables and their descriptions is given in Table 7.

Table 7.

The complete description of all variables in the database used for this study

Variable	Description
Manufacturer	Manufacturer of the car
Model	The exact model of the car
Year	The year the car was built
Type	What type of fuel does the car use; this can be either petrol, diesel, electric, or different types of hybrid
Price	The price of the car, in Euros
Fuel test	The fuel intensity during the road test by Quattroruote, measured in L/100 km
Fuel manufacturer	The fuel intensity of the car according to the manufacturer, measured in L/100 km
Fuel price	The fuel price at the time of the test, in Euros
Horsepower	The horsepower of the car, no unit
Cylinder	The engine size of the car, measured in cubic centimeters
CO2 test	The carbon dioxide emissions of the car during the test by Quattroruote, measured in g/km
CO2 manufacturer	The carbon dioxide emissions of the car according to the manufacturer, measured in g/km
Weight	The weight of the car (including the driver), measured in kg
Aerodynamic constant	A drag coefficient based on the frontal shape of the car, no unit
RPM at 130 km/h in the highest gear	The number of revolutions per minute the engine of the car needs to make to keep the car driving at a constant speed of 130 km/h, measured in 1/minute
Electric testa	The electricity consumption of electric cars during the test by Quattroruote, measured in km/kWh
Electric manufacturera	The electricity consumption of electric cars according to the manufacturer, measured in km/kWh
Journey lengtha	The distance that was traveled during the test by Quattroruote, measured in km
Journey timea	The time it took to perform the test drive, measured in hours and minutes
Journey speeda	The average speed during the test drive, a combination of the variables Journey length and Journey time. Measured in km/h
Temperaturea	The temperature during the test drive, measured in °C
Power-weight ratio	The power-to-weight ratio of the car, no unit
N/V ratio	The ratio between the RPM and the velocity at 130 km/h, no unit

^aThese variables were only for electric cars.

Note that not every variable was available for every car. The more expensive cars or brands tend to hide or limit the data that Quattroruote can publish about their cars. Furthermore, some variables were combined to make new variables. Examples are the power-to-weight ratio, the N/V ratio from the revolutions per minute (RPM) at 130 km/h measurement, and the average speed for electric cars calculated from the journey length and time. Since the variety of cars that are tested is very large, all the collected variables cover a large range. This gives a broad and credibly comprehensive perspective.

We used multivariate regression analysis to estimate the power rebound. The associations of vehicle fuel intensity with each of the parameters that influence it independently is given by:

$$logF=K-{\beta }_{1}Y+{\beta }_{2}logP+{\beta }_{3}logW+{\beta }_{4}logC+{\beta }_{5}logN+\mathrm{er}$$ 5

where $F$ = Fuel intensity [L/100 km], $Y$ = year, $P$ = rated engine power [hp], $W$ = weight [kg], $C$ = aerodynamic constant and $N$ = N/V ratio, er = other influences not accounted for in the model, K is a constant, and ${\beta }_i$, etc. are the coefficients of these variables as given by the multivariate analysis of the data.

This gave the association of (the log of) vehicle power, P, with the vehicle fuel intensity, separated out from the influences of the other variables (speed, weight, etc.). This is the power rebound effect, as in Eq. (2) in the section “Literature review.”

Multiple-linear regression

We therefore conducted a series of multiple-linear regression analyses on vehicle testing data to measure the impacts of multiple independent variables on a single dependent variable. The dependent variable, in this case, is energy intensity, given by the fuel consumption during the road test of Quattroruote. Using multiple-linear regression provides the opportunity to test the impacts of variables other than the rated power of a car. Therefore, the regressions initially included all the variables from Table 7. As explained below, by transforming most of the variables to their logarithmic values, the regression coefficient for each of the log-transformed variables gives a direct value of its rebound effect according to Eq. (1).

There are some differences between the study of road tests on freight trucks⁵⁵. First, some of the independent variables in this research are different. For example, in this study, aerodynamics is included because it plays a more important role in cars than in trucks. Second, regression analyses are performed for each fuel type. Almost all freight trucks use diesel as their fuel, whereas this is not the case for cars. Petrol and diesel engines are different in many aspects. They have different ways of combusting fuel, and diesel cars are, on average, more fuel-efficient than petrol cars. A third difference is that cars are classified by their weight. The regulations on vehicles in most European countries specify a passenger vehicle as any weight up to 3500 kg (Rijksoverheid, 2020). Therefore, a classification is made for this research, see Table 8.

Table 8.

Weight classes for personal cars

Class	Weight
Lightweight	<1500 kg
Mediumweight	1500–2000 kg
Heavyweight	>2000 kg

Log-log-linear regression

Log-log regression was used where feasible in this analysis for two reasons. First, the distributions of the values of most of the variables tended to be right-skewed. Using the log transformation gave distributions much closer to normal distributions. These give more accurate results in multivariate regression analyses. Second, in line with Eq. (1) above, with log transformations of both the dependent and independent variables, the regression coefficient is the rebound effect. For example, an independent variable with a regression coefficient of 0.3 means that each change of 1% in the value of that independent variable is associated with a 0.3% change in the value of the dependent variable (in this case fuel intensity) if all other independent variables are held constant. This would represent a rebound effect of 0.3, i.e., 30%. This gives a clear view of how percentage changes in variables, such as efficiency and power rating, affect consumption. Note, however, that it was not feasible to do a log transformation of the variable “year of manufacture” as this distribution is perfectly flat. The regression coefficient for this variable therefore means that each succeeding year is associated with a percentage change in energy intensity but not strictly a “rebound effect” as in Eq. (1).

The dependent variable in the regression analyses is (the log of) “fuel intensity”. We use the term “fuel intensity” rather than “fuel economy” as the parameter is given in terms of L/100 km. Fuel intensity increases as L/100 km increase, but fuel economy reduces as L/100 km increases. In the regression analyses, we consider independent variables to have a statistically “significant” impact on fuel intensity if their p value is ≤0.10. This means that there is a 10% probability or less that the sign (+ or −) of the regression coefficient in the population of all cars is zero or the opposite of that given in the regression analysis.

We first performed preliminary stepwise regression analyses, initially using all the independent variables listed in Table 7. Those showing multicollinearity or having large p values were eliminated at each stage, eventually giving a final list of 5 significant independent variables: year of manufacture, engine power, weight, aerodynamic drag coefficient (C), and N/V ratio. The final regression analyses, therefore, give the percentage change in fuel intensity for each 1% change in each of these dependent variables—except for the variable “year of manufacture,” as explained above.

Author contributions

K.H.: methodology, writing—original draft, validation. B.v.L.: data, methodology, validation. F.L.: conceptualization, supervision, analysis, writing—review and editing. R.G.: conceptualization, supervision, knowledge, writing—review and editing. R.F.: conception, supervision, writing—review and editing.

Data availability

The datasets supporting the findings of this study are available in a public GitHub repository titled “Rebound-effects-of-power-enhancement-in-internal-combustion-and-electric-vehicles” at: https://github.com/hk201200107/Rebound-effects-of-power-enhancement-in-internal-combustion-and-electric-vehicles.

Code availability

The code supporting the findings of this study is available in a public GitHub repository titled “Rebound-effects-of-power-enhancement-in-internal-combustion-and-electric-vehicles” at: https://github.com/hk201200107/Rebound-effects-of-power-enhancement-in-internal-combustion-and-electric-vehicles.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s44333-026-00082-8.