# Speed Limits

Speed 20mph limit and fuel consumption the facts

# Speed limits and fuel consumption

### Introduction

Some time ago I wrote by email to the Department of Transport (UK) querying what I had read on the Internet claiming as a fact that modern cars are not capable of being driven in high gear at speeds of 20 mph. I received a lengthy reply to my query which is published below along with my letter.

Hi

My understanding of trying to drive so as to consume less fuel and contribute less CO2 into the environment is to keep my speed down and keep my car’s RPM low as well. However, I have read this:

Slow and Dirty

Another issue is that slower speeds would increase pollution. This may seem counter-intuitive, but any vehicle with an internal combustion engine will need to be driven in a lower gear at 20 mph than at 30 mph. The revolutions per minute will be similar, but the revolutions per mile travelled will be half as much again, leading to an increase in fuel consumption and emissions. In fact, the gearing on typical modern vehicles (such as, for example, a 1.6 litre Ford Focus) is often such that they will cruise at 30 in fourth, but are only comfortable at 20 in second, so their rpm would actually be higher.

The extract is part of an argument to reject the increasing use of 20mph limits in residential areas.  My car a diesel land rover discovery is quite happy to roll along at almost tickover which is not much more than 1000 RPM. The car is an automatic. I don’t think that the sentiments expressed in the extract are correct.

The flaw in the first part of the argument is that it would only be valid if the car was forced to travel at a low speed.  The car would, indeed, be forced to travel at a low speed in a restricted area of a residential settlement. But to apply the rationale to driving at lower speeds in general is an error.  For example, in open country going down a hill, in which case the car would “roll” faster again at probably tickover RPM and reach a much higher speed than 20 MPH. My car would easily reach 45 MPH going down a moderate hill. Of course if I was constrained to travel at 20 MPH then either I would be braking � and wasting fuel or using a lower gear ratio as a lockup.

The flaw, in the second part of the argument is that a “modern” car is well designed when their use is largely in urban areas, rather than open country,  and should surely be designed to run happily at speeds of 20 to 30 MPH.  A modern car only emits CO2 an water, so one can hardly regard that as pollution, except in so far as it is considered that CO2 is damaging to the environment.

Whilst for family and work reasons I need a 4x4 and can’t afford to run a small car as well I am concerned to drive and use my car so as to aspire to sustainable Travel.

I would be please to receive a comment on my observations in relation to the above argument.

Thank you

Geoff Edwards

Department for

Transport

Simon Davies

Senior Engineer

CFV3

Department for Transport

Zone 1/34

Great Minster House

76 Marsham Street

London SW1P4DR

Direct Line: 020 7944 2116

Fax: 020 7944 2512

GTN No: 3533 2116

Web Site: www.Oftgov.uk

28 June 2010

Mr Geoff Edwards by email

Dear Mr Edwards.

## Speed limits and fuel consumption

Thank you for your recent enquiry, sent to our "sustainable travel" email address, which has been passed to me as an official in the Division with the most direct interest in vehicle emissions.

There are elements of truth in the argument against twenty mile per hour speed limits that you quote, but there are also, as you suggest, a number of flaws. I hope that you will excuse my rehearsing, below, some of the technical background to this argument.

I am strongly inclined to agree with your suggestion that modern cars are, in general, designed to run quite happily at thirty miles per hour in fifth gear, rather than in fourth gear as the article suggests. The suggestion, in the article, that it would be necessary to run such a vehicle in second gear if it were travelling at twenty miles per hour is certainly nonsense.

Whilst it is true that most of the emissions from a modern car are carbon dioxide and water vapour (plus, of course, nitrogen and any uncombined oxygen from the air that was drawn into the engine), there are still some emissions of air quality pollutants. Although these air quality pollutants form only a small fraction of the total exhaust emissions they are of considerable interest to us because they have significant public hearth implications, particularly in areas where traffic density is high or where there are other sources of pollutants.

The air quality exhaust pollutants that are currently regulated are oxides of nitrogen (NO,), carbon monoxide (CO), hydrocarbons (HC)( and particulate matter (PM) which is both visible and invisible smoke. Of these pollutants, it is oxides of nitrogen and particulate matter that are currently of the greatest concern since, partly as a result of the increasingly strict exhaust emissions standards which have been imposed upon manufacturers over the years, the United Kingdom has no exceedences of its air quality targets for atmospheric concentrations of either carbon monoxide or hydrocarbons. Exhaust emissions of lead and lead compounds are controlled by limits on the amount of lead permitted in fuel, and you will be aware that all generally available road transport fuel is now effectively lead-free.

Whilst emissions of carbon monoxide, of hydrocarbons, and of particulate matter are, in general, the result of incomplete combustion of the fuel (or of lubricating oil drawn into the cylinder), oxides of nitrogen are formed when oxygen and nitrogen from the air are brought together at high temperatures. This means that emissions of oxides of nitrogen from the engine itself (though, because of aftertreatment systems such as catalysts, not necessarily from the exhaust pipe) tend to be higher when the engine is working most efficiently, whilst emissions of the other pollutants tend to be higher when the engine is working less efficiently.

It is certainly true that changing to a lower gear at any particular speed will generally increase fuel consumption, and will be liable to increase emissions of some air quality pollutants from the engine. Whilst the relationship between fuel consumption and emissions of carbon dioxide is quite simple (with one litre of petrol producing 2.3 kilogrammes and one litre of diesel producing 2.64 kilogrammes of carbon dioxide) the relationship between fuel consumption and emissions of air quality pollutants either from the engine itself or from the exhaust pipe is quite a complex one.

The question of fuel consumption comes down, at a simple level, of course, to one about the amount of energy expended in moving the vehicle. This amount of energy may be calculated simply by multiplying the force required to move the vehicle by the distance over which the vehicle is moved. A particular fuel, meanwhile, will have a characteristic calorific value, and hence a characteristic energy content per litre or per kilogramme, or per gallon or per pound mass if you are working in Imperial units. (For petrol, this energy content is approximately 32.2 Megajoules per litre, and for diesel fuel it is about 35.9 Megajoules per litre.)

It follows from the argument above that the amount of fuel used in moving a vehicle will be directly proportional, in a simple theory, to the distance travelled and the resistance to motion experienced by the vehicle. Consideration will have to be given, in working out how much fuel wilt actually be consumed, to the efficiency with which the engine converts the chemical energy in the fuel into mechanical work. A figure of about thirty percent for this efficiency of conversion is a reasonable rule of thumb for a petrol engine, but the actual figure will depend upon engine speed and load and will vary somewhat from one engine model to another.

The resistance to motion experienced by the vehicle on a level road is made up of two elements. These two elements are simple rolling resistance, and aerodynamic drag.

The simple rolling resistance is due to such things as flexing of the tyres, scrub of the rubber on the road, and friction in the wheel bearings. The simple rolling resistance tends to be proportional to the vehicle weight, and tends not to rise very much with increasing speed. For cars, the simple rolling resistance usually lies in the region of one percent of the vehicle weight (in Newtons, for the purposes of calculations in SI units, where a mass of one kilogramme involves a weight of 9.81 Newtons) and this figure can reasonably safely, for rough working, be assumed to be the same at all speeds.

Aerodynamics is a complex science, but, because compressibility effects and variations in Reynold's number can be safely ignored over the range of speeds that are of interest, the approximate aerodynamic drag on a road vehicle may be calculated using the formula;

Fd = 0.5CdAp V2

where;

Fd  is the drag force in Newtons.

Cd is the drag coefficient for the moving vehicle.

A is the cross sectional area of the vehicle presented to the airflow, in square metres.

p is the density of the air (1.2 kg/m3).

V is the speed of movement, in metres per second.

Modern motor cars tend to have drag coefficients a little above 0.3 {so that the aerodynamic drag on them is about one third of what it would be upon a sheet of plywood presenting the same frontal area) although the drag coefficient of a car like a Land Rover would be rather higher.  Examination of the formula shows that, if the other factors remain constant, the aerodynamic drag force is proportional to the square of the speed. This means that doubling the speed results in four times the aerodynamic drag.  It means that a vehicle is experiencing sixteen times more aerodynamic drag at eighty miles per hour than it was at twenty miles per hour.  It follows that decreasing the speed to fifty from seventy miles per hour approximately halves the aerodynamic drag.

By a speed of about fifty miles per hour the aerodynamic drag is becoming the dominant element in the resistance to motion experienced by the average car. if we chose to say that aerodynamic drag and simple rolling resistance were equal at fifty miles per hour, then our calculations would suggest that a vehicle travelling at seventy miles per hour would be experiencing about one and a half times the total resistance to motion, and so be using fuel at about one and a half times the rate, that it was at fifty miles per hour.

Although there is a very rough rule of thumb that says that, of the energy released by burning the fuel in a piston engine, one third goes to the coolant and is lost as heat from the radiator, one third is lost as heat in the exhaust gases, and one third produces useful work, in practice, for a variety of reasons, the thermal efficiency of an internal combustion engine does vary, as I mentioned above, over its operating envelope.

The graph that I have included below, and have added to the attached Microsoft Word document so that you will be able to view it in colour, shows a somewhat idealised version of the fuelling map for a fairly typical petrol engine. The overarching curve that forms the upper boundary to the map in both cases is the full-throttle torque curve for the engine, and so represents the maximum torque that can be extracted from the engine at any particular engine speed. Maps of this kind are produced either on a test bed, with the engine loaded using a dynamometer in order to record its fuel consumption both on the full-throttle torque curve and at a very large number of speed and toque points beneath it, or with the aid of very sophisticated modelling software. The contour lines on the map would normally be labelled as lines of equal specific fuel consumption (in grammes of fuel per kilowatt hour of engine output energy, or some equivalent unit) but the Dutch researchers to whom I am indebted for the idealised map have converted the contours in their map to lines of equal thermal efficiency.

A feature of the fuelling map is that there is an "eye," just below the maximum torque speed, where the engine is most fuel efficient The map shows that the efficiency of the engine is quite poor when it is running lightly loaded at any speed, and so underlines the importance of purchasing a vehicle with an engine which has an appropriate, and not an excessive, nominal power output.

### Fuel map

The two points marked 'A' and 'B' on the fuelling map were originally added for another purpose, but serve to illustrate the value, in fuel efficiency terms, of driving in the highest gear that the engine will comfortably permit.

The two marked points actually lie on a constant power curve, and are both points where the engine is producing about five kilowatts. I think that the figure of five kilowatts (6.7 horsepower) was chosen as representing approximately the power required to drive an average car at a steady speed of about thirty miles (fifty kilometres) per hour.

At point 'A' the vehicle is being driven in a high gear where the engine is running at hardly more than tickover speed, whilst at point 'B' it is being driven at the same road speed in a lower gear. It is clear from examination of the fuelling map that driving in the lower gear, although it makes the engine run at a speed closer to the maximum torque speed, involves running the engine at an operating point where it is less efficient because it is more lightly loaded. (The situation is, in fact, rather worse than the fuelling map suggests, since lower gears and higher engine speeds are usually associated with higher gearbox losses and higher parasitic losses from engine auxiliaries.)

Although the analysis above supports an argument that changing to a lower gear unnecessarily at any particular speed is likely to be a mistake from an environmental impact point of view, it does not necessarily support an argument that slowing down to such an extent as to require changing to a lower gear is also a mistake. Whilst changing to the lower gear in the diagram moves the engine operating point from point 'A' to the less efficient point 'B', for instance, and slowing the vehicle would then move the operating point leftwards and downwards towards an even less efficient operating point, it has to be remembered that diagrams of this sort are expressed in "specific" terms, and that using more fuel per unit of energy required at the wheels will not require more fuel in absolute terms if the energy required at the wheels goes down at the same time.

I suspect that, in reality, if travelling at steady speeds were the only thing that cars actually did, then slowing a typical saloon car from a steady thirty to a steady twenty miles per hour, and changing to a lower gear, might actually be environmentally disadvantageous. This is because the change in resistance to motion between the two speeds would be small for a car with a low drag coefficient. It does not follow, however, either that slowing from, say, 3 steady fifty miles per hour to a steady twenty miles per hour and changing to a lower gear would also be environmentally disadvantageous, or that slowing from thirty to twenty miles per hour would be environmentally disadvantageous in a vehicle with a higher drag coefficient.

Some of the claims that are made to the effect that lower speeds lead to increased fuel consumption and increased emissions are based upon a misreading of the data on emissions that is presented on the websites of the Department and of its agencies. This is because the data shows that emissions in grammes per kilometre travelled rise steeply at low speeds. The data refers, however, not to vehicles travelling at steady speeds but to vehicles in traffic streams travelling at the average speeds given. The emissions rise at lower speeds in these cases because it is assumed that a vehicle in a traffic stream travelling at an average speed of ten miles per hour, for instance, is having to stop and start far more frequently than one in a traffic stream travelling at an average speed of thirty miles per hour. The data presented is not intended to reflect what is possible or what can be achieved by the application of skill on the part of an individual driver, but what currently happens to the average vehicle in a real traffic stream.

Whilst the effect of steady speed upon fuel consumption is significant, the choice of a steady cruising speed under circumstances where a steady speed can be maintained is only one of the aspects of driver behaviour that affect fuel consumption on real journeys. Research shows that a driver who thinks ahead, and drives more smoothly and steadily, is likely to complete the same journey, in the same time, for rather less fuel consumed than is his or her less skilled counterpart who (often under the mistaken, if understandable, impression that a higher average speed will necessarily be achieved by always driving as fast as possible) engages in a great deal of unnecessary acceleration and braking. Unnecessary braking simply turns the kinetic energy stored in the moving vehicle into heat and into brake dust and then leads, inevitably, to unnecessary acceleration. The more highly skilled driver achieves an identical journey time whilst using less fuel simply by matching the speed of his or her vehicle more closely to the average speed of the traffic.

Although a vehicle with four-wheel drive will necessarily be somewhat heavier, and will be likely to have slightly higher transmission losses, than an equivalent two-wheel drive vehicle (as a consequence of having the transmission components required to get the drive to the additional wheels) the simple fact of a vehicle having four-wheel drive is not really of any environmental significance. In environmental terms the aspects of a vehicle that are important are largely the ones such as mass, aerodynamic drag coefficient, nominal power to weight ratio, and the unnecessary use of power-hungry ancillaries like air conditioning, which impinge upon fuel consumption. Cars with conventional automatic transmissions, as you will be aware, tend to have higher transmission losses than those with manual transmissions. The largest single factor in the fuel consumption and environmental impact of a car, however, is, as you suggest, the behaviour of the driver.

I hope that this is of assistance.

Yours sincerely,

Simon Davies

Posted on 19 Aug 2013 by Geoff Edwards

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