Background

Urban road transport is remarkably inefficient. Average traffic speeds in London are 7.4mph – slower than they were in the days of the horse and cart. Most car journeys would be quicker if you ran. Yet the costs to run and fuel a vehicle, and the CO2 emissions, traffic deaths and injuries and air pollution from urban road transport are large.

Understanding the effect of speed on emissions in an urban environment.

Skyrad used an innovative approach to model the effect of maximum vehicle speeds in typical urban traffic. We found that higher peak vehicle speeds (the maximum speed reached by vehicles in between junctions) adversely affected CO2 and NOx emissions, while having only a small effect on total journey times.

The effect of maximum speed on CO2 and NOx emissions were substantial. The emissions were dominated by the energy required to accelerate the vehicle in stop-start traffic. This contrasts to many of the accepted models in the literature, which exclude the effect of stop-start traffic and consider only the ‘cruise’ portion of the journey.

We modelled 3 different vehicles, a small hatchback (Ford Focus), a large SUV (Range Rover Discovery) and a van (Ford Transit). Note that due to the availability of engine model data, CO2 is modelled for a petrol vehicle, NOx is modelled for a diesel.

CO2 emissions at a 30 mph max speed were found to be 42% higher than at 15mph, and 35% higher than at 20mph.

NOx emissions at a 30 mph max speed were 25% higher than at 15mph, and 39% higher than at 20mph.

The effect on journey times were also modelled. A maximum speed of 20mph reduces the average journey speed by 8% compared to a a maximum speed of 30mph.

Summary

The simulation models the driving behaviour, speed, fuel consumption and emissions of vehicles in stop-start traffic that is typical of driving in London or a similar busy city.

The aim of the simulation is to see the effects of accelerating to different maximum speeds, taking into account the effects of traffic.

The question addressed is: If vehicles drive up to the speed limit whenever the road in front of them is clear, how does that speed limit effect their emissions, average speed and drive time? It does not attempt to measure driver behaviour – how fast drivers tend to drive in different speed limits. This will be different, as not every driver will drive at the speed limit – some will drive slower than the limit and some will exceed it.

The traffic was modelled as a queue of identical vehicles that crossed a series of traffic lights, which each represent hitting a junction, pedestrian crossing, vehicle in front turning or other obstruction or reason to slow down. The spacing of the traffic lights was set to 160m, based on Google Street view maps of a series of large London roads (A23, A2, A315, A219) and on driving round London in different traffic conditions during different times of the day and counting the number of times per mile the traffic caused the vehicle to either stop or drop below 5 mph. The average number of stops per mile driven was 10, equivalent to a junction every 160m. In terms of emissions, a drop to 5mph or lower is approximately the same as coming to a complete stop.

A queue of 100 vehicles was then modelled driving the route. The vehicles start from a stationary start, and stop when they hit a red light or to maintain the distance to the vehicle in front. The 95th vehicle in the queue is taken as the representative vehicle of being in fully developed traffic (i.e. not the first vehicle on the road in the morning).

The simulation is repeated 50 times with different random traffic light phasing. For each vehicle the energy required is calculated based on the mass, rolling resistance, coefficient of drag and frontal area. The energy required is then mapped via a gearbox ratio model for that vehicle, and the torque and rpm used to look up the brake specific fuel consumption for that engine from engine maps published by the US EPA https://www.epa.gov/vehicle-and-fuel-emissions-testing/combining-data-complete-engine-alpha-maps . Note that the maps are for petrol vehicles. We do not have equivalent maps for diesel engines.

The number of stop-starts is different for each simulation, due to the random phasing of the traffic lights.

The traffic light duty cycle was adjusted to give an average speed of 7.4mph (based on TfL published average traffic speed) at 30mph maximum speed.

The model was animated to show the interaction between maximum speed and queuing. Typically vehicle progress is only intermittently affected by speed. Most of the time the vehicle is in the same place in the queue for the next set of lights. Only occasionally does a higher speed permit the vehicle to pass the next lights on green.

A video of the simulation is available to view here:

http://videos.futuretransport.info/cars_15_20_30_test_car96.mp4

Of note was that one of the major drivers of average speed was vehicle size and headway through the lights. Smaller vehicles with a lower top speed has a faster average speed. If everyone in London drove a golf buggy with a top speed of 15mph, average speeds would be around 8.9mph compared to 7.4mph for full size vehicles doing 30mph. This can be seen in this simulation.

http://videos.futuretransport.info/cars30_V_buggys15mph_RangeRovers.mp4

The CO2 model was validated by a simple empirical test. We set up a 2km stretch of empty road, and accelerated to the maximum speed 14 times (equivalent to stopping every 140m) and measuring the average mpg using the trip computer on the vehicle. The vehicle was a 2.2l diesel Toyota Verso.

Table 1: Fuel Efficiency and CO2 production results relative to  a maximum speed of 30mph.

Max Speed (mph) Fuel Efficiency (MPG) CO2 at 30mph Max Speed was
15 38.5 93% higher than at 15mph
20 32.1 61% higher than at 20mph
30 20.0

Results

Breaking the energy consumed by stage of driving down shows the dominant effect of the energy required to accelerate the vehicle. Energy consumed during cruising varies with speed. The gear ratios on most vehicles are chosen to reduce the emissions while cruising at 30mph as this is where the NEDC emissions tests are performed. However at higher speeds, the energy required to accelerate the vehicle in stop start traffic outweighs any reduction in the emissions during cruising.

Figure 1: Energy consumed over the same journey at speed limits of 15mph, 20mph and 30mph, and the breakdown of the energy consumed in accelerating, decelerating, cruising and stationary phases.

Figure 2: Velocity of the 95th vehicle throughout the journey at speed limits between 5mph and 50mph, averaged across 50 different simulations.

Figure 3: Time required by the 95th vehicle to complete the journey at speed limits between 5mph and 50mph, averaged across 50 different simulations.

Figure 4: Fuel efficiency achieved by the 95th vehicle over the journey at speed limits between 5mph and 50mph, averaged across 50 different simulations.

Figure 5: CO2 emissions per kilometre of the 95th vehicle over the journey at speed limits between 5mph and 50mph, averaged across 50 different simulations.

Figure 6: NOx emissions per kilometre of the 95th vehicle over the journey at speed limits between 5mph and 50mph, averaged across 50 different simulations.

Table 2: Results of the simulations for a Range Rover Discovery.

Speed Limit (mph) Mean Velocity (mph) Mean Time (s) Mean Energy (J) Fuel Consumed (l) MPG Mean CO2/km (g/km) Mean Nox (ppm) Mean Nox/km (g/km)
5 2.58 1212.1 1.27E+07 0.366 10.68 633.21 13.85 0.0434
10 4.71 668.5 1.02E+07 0.294 13.30 508.60 10.70 0.0270
15 6.13 519.2 8.53E+06 0.247 15.86 426.29 8.07 0.0170
20 6.82 467.4 8.35E+06 0.242 16.20 417.42 6.67 0.0138
25 7.11 447.8 9.64E+06 0.279 14.04 481.64 6.71 0.0160
30 7.35 435.3 1.08E+07 0.312 12.53 539.74 6.36 0.0170
35 7.43 430.6 1.20E+07 0.346 11.30 598.67 6.42 0.0191
40 7.46 429.2 1.24E+07 0.358 10.93 618.91 6.34 0.0195
45 7.43 431.2 1.28E+07 0.371 10.55 641.10 6.41 0.0204
50 7.41 431.9 1.30E+07 0.377 10.38 651.45 6.43 0.0207

Table 3: Results of the simulations for a Ford Focus.

Speed Limit (mph) Mean Velocity (mph) Mean Time (s) Mean Energy (J) Fuel Consumed (l) MPG Mean CO2/km (g/km) Mean Nox (ppm) Mean Nox/km (g/km)
5 2.58 1212.0 6.01E+06 0.174 22.52 300.27 6.79 0.0101
10 4.71 668.5 5.44E+06 0.157 24.89 271.67 6.06 0.0082
12.5 5.59 566.5 3.55E+06 0.103 38.14 177.33 3.77 0.0033
15 6.13 519.2 3.68E+06 0.106 36.75 184.04 3.79 0.0035
17.5 6.50 489.7 3.91E+06 0.113 34.65 195.18 3.89 0.0038
20 6.82 467.4 3.53E+06 0.102 38.38 176.20 3.22 0.0028
25 7.11 447.8 4.17E+06 0.121 32.47 208.27 3.37 0.0035
30 7.35 435.3 4.74E+06 0.137 28.53 237.06 3.32 0.0039
35 7.44 430.6 5.36E+06 0.155 25.23 268.01 3.44 0.0046
40 7.46 429.2 5.62E+06 0.163 24.08 280.89 3.47 0.0048
45 7.43 431.2 5.85E+06 0.169 23.12 292.53 3.52 0.0051
50 7.41 431.9 5.97E+06 0.173 22.67 298.33 3.53 0.0052

 

Model Details

Vehicle Motion

The model allows a vehicle to accelerate if the gap to the vehicle in front increases beyond 3m (8m front bumper to front bumper for a 5m long vehicle). The vehicle then begins to accelerate according to the following equation, where is v the velocity, a is the acceleration rate of 0.7m/s2, Δt is the duration of the model time step, n indicates the current time step and n-1 indicates the previous time step:

The vehicle accelerates until it reaches the designated speed limit. Once at the speed limit it maintains a constant velocity until it needs to slow down due to a red light or a slowing car.

A stopping distance for each vehicle at their current velocity is calculated. This is based on rule 126 of the UK Highway Code [1] which gives a general guide for stopping distances at different speeds. This stopping distance accounts for braking distance and thinking distance which accounts for the driver’s reactions time to a situation which requires them to stop.

Figure 7: Stopping distance guide for a vehicle according to rule 126 of the UK Highway Code [1].

If a vehicle is approaching a red light without another vehicle in front of it, then it slows according to the following equation, where vstart is the velocity at which the vehicle begins to slow down, dto lights is the vehicle’s current distance to the lights, dstopping is the stopping distance interpolated from stopping distances in Figure 1, and dmargin to lights is the distance from the lights at which the vehicle will stop (default 1m):

The 2/2.24 term makes it so that the vehicle will be at 2mph when it reaches dmargin to lights. Once the vehicle reaches 2mph, it’s velocity is instantly reduced to 0mph. This prevents the vehicle from asymptotically approaching the lights.

If the traffic light is about to change to red and the stopping distance for the vehicle at its current velocity is less than the distance to the lights, then the vehicle cannot slow down in time for the lights. Instead, the vehicle will not slow down and will instead carry on through the lights. This is to simulate the amber phase of the traffic lights.

A vehicle will start to slow down if it approaches another slowing vehicle. This occurs once the distance to the vehicle in front, dto car in front, gets within 3m + dstop gap, and when this distance is reducing. dstop gap is the gap that the cars maintain to one another when stopped (default 7m). When this happens, the vehicle behind begins to slow down to the speed of the vehicle in front. As the happens, the gap between the vehicles reduces to the stop gap. The vehicle slows down in accordance with the equation below, where vcar in front is the velocity of the car immediately in front of the vehicle in question:

Vehicle Position

Knowing the velocity of the vehicle allows the distance travelled over the current time step to be calculated from the following, where x is the vehicle position relative to a common start point, and Δt is the time step of the simulation:

Force to Move

At each time step, the force required to achieve the motion previously calculated is determined. The force to overcome the air resistance is calculated from the following, where Fd is the drag force, cd is the coefficient of drag for the vehicle, ρ is the density of air and A is the characteristic frontal area of the vehicle:

The force to overcome the rolling resistance is calculated from the following, where Fr is the rolling resistance, p is the tyre pressure, m is the mass of the vehicle and ag is acceleration due to gravity.

If the vehicle is at a constant velocity, then the force required to maintain that velocity is the force required to overcome the air resistance and rolling resistance being experienced by the vehicle.

If the vehicle is accelerating, then the then the force required to accelerate, Fa, must also be accounted for:

The total force to accelerate is the sum of these 3 forces:

Chosen Gear

Knowing the vehicle velocity and the characteristics of the vehicle’s drivetrain allows the engine speed to be calculated. The vehicle’s all start in first gear and shift up a gear when their engine speed goes above a defined threshold for that vehicle. There are 2 different thresholds for shifting up. If the vehicle is still accelerating, then it will shift up when it exceeds the upper up-shift threshold (default 2500 RPM). If the vehicle is not accelerating (i.e. it has reached the speed limit), then it will shift up when it exceed the lower up-shift threshold (default 2000 RPM). The upper up-shift threshold allows the vehicle to utilise more engine torque when required for acceleration.

The vehicle will shift down a gear when its engine speed drops below the defined down-shift threshold (default 1000 RPM). The vehicle will also shift down as many gears as required if it cannot achieve the required torque in its current gear.

With the current gear known, the engine speed is calculated from the following, where ωRPM is the engine speed in revolutions per minute, GR is the gear ratio of the current gear, FD is the final drive ratio of the transmission and r is the radius of the wheel:

Energy

The power required, P, is calculated from the force required to move, the vehicle velocity and the overall efficiency of the vehicle, η, which is assumed to be 0.9 to account for drivetrain loses:

From this power and the engine speed, the torque, T, required from the engine is calculated:

With a known engine speed and required torque, the fuel consumption rate can be determined by interpolating the engine’s brake specific fuel consumption (BSFC) map. In this model, 2 different engines were modelled, the 2013 Ford 1.3l EcoBoost engine [2] and the 2015 Ford 2.7l EcoBoost engine [3]. Each engine has its own BSFC map. The BSFC map allows the fuel consumption rate of the engine to be determined for a combination of engine speed and torque.

Figure 8: Brake Specific Fuel Consumption map for the 2013 Ford 1.6l EcoBoost Engine [2].

Figure 9: Brake Specifi Fuel Consumption map for the 2015 Ford 2.7l EcoBoost Engine [3].

If the required torque and current engine speed is unachievable (i.e. it is outside the bounds of the BSFC map) then the vehicle shifts down by 1 gear, resulting in a higher engine speed and lower torque which is achievable.

From the fuel consumption rate, f, the energy consumed, E, can be calculated from the calorific value of petrol, Epet (45.8×106 J/kg):

If the vehicle is idling rather than moving, the energy is calculated from the following, where Veng is the engine capacity and fidle is the idling fuel consumption rate:

The energy used throughout the journey is the sum of the energy used at each time step as calculated from the equations above.

CO2 Emissions

CO2 emissions is directly proportional to fuel consumption. Fuel consumption is known from the fuel consumption rate previously determined. 2932g of CO2 is produced per litre of petrol burned, such that the total CO2 emissions per kilometre can be calculated from the following, where Vpet is the volume of petrol in litres and  is the total distance travelled by the vehicle over the journey:

Vehicle Properties

The table below details the properties of the vehicles used. 2 engine models were used, and for each vehicle the engine which most closely match that of the vehicle was used.

Table 4: Properties for the vehicles used in the traffic simulation model.

 Model Engine Model Used in Sim Vehicle Mass (kg) Drag Coefficient Frontal Area (m2) Tyre Pressure (psi) Wheel Diameter (in) Final Drive Ratio Gear Ratios
2019 Ford Focus 1.5 EcoBoost [4] 2013 Ford EcoBoost 1.6l 1294 0.273 2.2 31 17 4.313 [3.583, 1.952, 1.29, 0.971, 0.775, 0.651]
2016 Range Rover Discovery 4 [5] 2015 Ford EcoBoost 2.7l 2565 0.4 3 31 19 3.317 [4.714, 3.143, 2.106, 1.667, 1.285, 1, 0.839, 0.667]
2016 Ford Transit Connect XLT Wagon 1.6l EcoBoost [6] 2013 Ford EcoBoost 1.6l 1819 0.35 2.81 31 16 3.51 [4.584, 2.964, 1.912, 1.446, 1, 0.746]
2016 Ford Transit Connect XLT Wagon 2.5l [7] 2015 Ford EcoBoost 2.7l 1819 0.35 2.81 31 16 3.21 [4.584, 2.964, 1.912, 1.446, 1, 0.746]

email comments to: transportanalysis@skyrad.co.uk

References

[1] UK Department for Transport. 2015. The Highway Code. [online] Available at: https://www.gov.uk/guidance/the-highway-code

[2] Ann Arbor MI: US EPA National Vehicle and Fuel Emissions Laboratory. 2018. 2013 Ford 1.6L EcoBoost Engine Tier 2 Fuel – ALPHA Map Package. [online] Available at: https://www.epa.gov/sites/default/files/2018-12/2013-ford-1.6l-ecoboost-engine-tier-2-fuel-alpha-map-package-10-25-18.zip

[3] Ann Arbor MI: US EPA National Vehicle and Fuel Emissions Laboratory. 2018. 2015 Ford 2.7L EcoBoost V6 Engine Tier 3 Fuel – ALPHA Map Package. [online] Available at: https://www.epa.gov/sites/default/files/2019-12/2015-ford2.7l-ecoboost-v6-engine-tier3-fuel-alpha-map-package-dated-11-27-19.zip

[4] automobile-catalog. 2021. 2019 Ford Focus 1.5 EcoBoost (182) (man. 6) (ST-Line) (model for Europe) car specifications & performance data review. [online] Available at: https://www.automobile-catalog.com/car/2019/2740310/ford_focus_1_5_ecoboost_182.html

[5] automobile-catalog. 2021. 2016 Land Rover Discovery 4 3.0 SCV6 (aut. 8) (model up to December 2016 for Europe Australia) car specifications & performance data review. [online] Available at: https://www.automobile-catalog.com/car/2016/2045465/land_rover_discovery_4_3_0_scv6.html

[6] automobile-catalog. 2021. 2016 Ford Transit Connect XL Wagon 2.5L lwb (aut. 6) (model for North America) car specifications & performance data review. [online] Available at: https://www.automobile-catalog.com/car/2016/1920530/ford_transit_connect_wagon_1_6l_ecoboost_lwb.html

[7] automobile-catalog. 2021. 2016 Ford Transit Connect XL Wagon 2.5L lwb (aut. 6) (model for North America) car specifications & performance data review. [online] Available at: https://www.automobile-catalog.com/car/2016/2079050/ford_transit_connect_xl_wagon_2_5l_lwb.html