In previous articles we've looked at some of the limitations of dyno testing of engine power. To recap briefly:

Engine dynos should be capable of very high accuracy in the measurement of flywheel bhp - easily within a couple of % or so. The main problem lies in the amount of care taken to ensure that the engine is tested in exactly the same state as it will be when installed in the vehicle. Often the car's full exhaust system is not used, sometimes because of space limitations in the dyno cell. The manifold may just be plumbed into a dyno exhaust system which doesn't sap as much power as the car's system. Also the coolant and inlet air temperatures may not be the same as in actual service and all ancillaries such as alternator, power steering pumps etc might not be fitted. Those awful temperature corrections rear their ugly heads quite often too. So the test may well be a very accurate measurement of the bhp of the engine in the dyno cell but considerably optimistic as regards the true installed power.

Rolling road dynos are much less accurate due to tyre slip, general calibration issues, unrealistic temperature compensations added to the measured power and also they can only tell you the bhp at the driving wheels. Most of the time this wheel bhp will still be accurate to within 5% or so though unless there has been tyre slip on the rollers. In general the estimates that operators, or the equipment, make for the amount of power added to the measured wheel bhp to estimate what the flywheel bhp might be is excessive. Most cars lose no more than 15% of the flywheel power in tyre and transmission losses but often as much as 30% or more is added to the wheel bhp by the operator to give you a vastly overinflated flywheel bhp figure. Good for bragging in the pub but it doesn't make the car any quicker.

Finally, remember that many supposedly measured power figures are just bare faced lies anyway. The accuracy of the dyno is of very little relevance if the engine never really got put onto it. I've seen plenty of cases like that in my time.

So is there an alternative to either of these methods that can give you a realistic measurement of the actual true installed power?

Well according to no less an authority than Sir Isaac Newton there is such a way. He deduced the universal laws of motion that determine how a body reacts to the forces imposed on it. The summary of those laws is that Force = Mass x Acceleration (F=M x A)

In other words if we know the mass of an object and the forces acting on it we can calculate how it fast it will accelerate. Or to put it another way - if we know the mass and how fast it accelerates then we can calculate the forces. A force of one Newton will cause a mass of one Kg to accelerate at one metre per second per second. Now this is all very well when only a single force and a point mass are being considered but how applicable is it to the acceleration of a vehicle? Certainly the forces acting on a vehicle are much more complicated but they are by no means impossible to calculate. In fact the majority of them are very simple. Plus we don't have to work it all out on bits of paper these days. Computer power makes complicated calculations like these a matter of seconds once the initial programming has been done. About 10 years ago I decided to write a programme like this myself and that started me down a long road of understanding how all the forces on a vehicle acted and how to simulate them. My own programme is actually a very complex spreadsheet, partly because I used to do a lot of spreadsheet programming and partly because I haven't got a clue how to programme in anything else which did kind of act as the deciding factor :) What you use to write the programme in matters less than whether the algorithms are correct of course. My own system doesn't have any fancy graphical displays, real time rev counters and little car icons whizzing up and down but it'll accelerate a car from rest to its top speed and be accurate to within a few tenths of a second and a few tenths of a mph at the 1/4 mile or any other point and that's the bit that matters most to me.

The primary consideration is one of how the engine power resolves into a force that accelerates the mass of the vehicle. We already know that one bhp is 33,000 foot pounds per minute and that power and torque are related by the equation: BHP = Torque x rpm / 5252. At a given rpm if we know the power then we also know the torque by definition. All we need to do to turn torque into driving force is multiply by the gearing and divide by the tyre radius. So for example, if an engine is producing 100 ft lbs of torque at the flywheel and the total gearing (final drive x gearbox ratio) is 10 : 1 then the torque at the driving axle is 1000 ft lbs. Torque is simply Force x Distance and the distance in question is the tyre radius. If the tyre radius is one foot then the force at the contact patch with the ground is 1000 lbs. Along the way there will be transmission losses where part of the power is absorbed in the gearbox and tyres. These issues are examined later on.

Starting from the full power or torque curves of the engine with respect to rpm, and by knowing the gearing and tyre size we can calculate the driving force in every gear at any road speed. That takes care of all the accelerative forces involved but there are also retarding forces to consider. The primary ones are aerodynamic drag and rolling resistance (drag in the tyres and wheel bearings etc). Both of these have been examined in the article on how power and speed are related which you can access here. Aerodynamic drag factors are published for many vehicles and can be estimated for most others with an intelligent appraisal of body size and shape. They only start to become critical at very high speed though and have little impact on 1/4 mile times and speeds for most vehicles.

Flywheels, crankshafts, wheels and tyres etc have to be accelerated both linearly along with the rest of the chassis and also in rotation which absorbs additional energy. If the moment of inertia of all these items is known then the energy they absorb can also be calculated. The problem, for any given vehicle, is knowing what the inertias really are without having to measure everything. Fortunately these items aren't enormously significant in comparison with the mass of the vehicle itself so a few simplifications can get you fairly close. In my own programme I split the masses into two main items - everything that rotates at engine speed (crank, flywheel etc) and everything that rotates at wheel speed (wheels, tyres, driveshafts). The few items that rotate at other speeds like camshafts and gearbox internals are so minor as to not affect the programme in any perceptible way. Having measured the inertia of these two main items for a few selected vehicles I can now estimate what they are likely to be for any other vehicle. Even a large error in these estimations will only have a minor impact on the overall acceleration.

A very simple approach is to just add 7% to the mass of the vehicle which will get you in the ballpark for most cars and this is how I used to do things before I added full inertia calculations to my programme. The problem with this simple approach is that items which rotate at engine speed have their greatest effect on acceleration in the lower gears. The article on flywheel lightening looks at this. So just adding a fixed amount to the vehicle mass will lead to the simulated acceleration being too fast in the lower gears and too slow in the higher ones. The accuracy of my own programme improved significantly when I included proper inertia calculations.

Gearchange time

Tyre grip

Headwinds or tailwinds

Up or down gradients

Maximum or minimum engine rpm limit

Clutch slip rpm to get the vehicle off the line

All of the above can be accounted for with additional programming in fairly simple ways. My own programme gets the car off the line in a very simple fashion. It doesn't use any complex clutch engagement strategies. It just asks for a clutch slip rpm and uses the torque at that rpm to start accelerating the vehicle. When the real rpm catches up to the clutch slip rpm it reverts back again. The second, and only other part of the starting strategy is a tyre grip limit expressed as a g force. If the calculated potential acceleration is greater than the grip limit then the programme just uses the grip limit until the potential acceleration drops back below it. I can adjust this grip limit until the simulation reaches the 60 foot mark (or 30 mph mark) in the same time as the real car did at the drag strip, which takes into account everything I need to know about the tyre and track conditions on the day. So it's no use someone saying my horsepower calculations were wrong because they had crappy tyres on that day or it was raining and therefore they didn't set a very good time due to lack of grip because the programme has already taken their actual grip into account. I can then increase the grip limit of course to see how much faster they could have gone under different conditions. If I'm not testing against an actual measured car's times then I take my best guess about grip. FWD cars on decent road tyres tend to leave the line at about 0.5g to 0.55g. RWD cars manage 0.6 or 0.65 and really light cars with plenty of rubber on the road like Westfields manage 0.8g in good conditions. 4wd road cars can exceed 1g and Pro Stock or Top Fuel drag cars on special wrinkle wall drag slicks leave the line at 3g or so which should give you some idea of the forces involved. To put it into perspective that's 6 times more acceleration than dropping the clutch on a fast fwd hot hatch which feels fast and violent enough to most people. At 3g you reach 60 mph in under 1 second and 100 mph in under 2.

There are some fairly complex aspects to how rotating components like the crank and flywheel store energy when the car is revving on the start line and then release it as the clutch is dropped. I've looked into these factors and they can alter the 0-60 mph time by about 0.1 of a second but I didn't feel it was worth building them into the programme for the sake of the work involved. It's worth realising they exist though if you intend to write your own.

The programme changes gear automatically when the next gear up becomes faster but it won't allow the revs to exceed the limit I type in. I can lower that limit below what the engine really wants to go to though to see how much effect there is on acceleration by short shifting. I added headwinds and gradients fairly recently - well a few years ago anyway. I can't remember exactly why but I think it might have been because of a magazine test where they thought the results were unrealistic because of a very high wind. I wondered how much difference wind conditions made to a real car so I added another couple of lines of programming to find out. The answer is that a 10 mph headwind for example, only reduces a car's top speed by about 4 or 5 mph and makes very little difference to the 1/4 mile time. Only 0.1 seconds or so although it reduces the terminal speed by about 1 mph.

With all of the information above it is possible to calculate very accurately how a vehicle will accelerate. There are various ways though in which the calculations can be performed. My own programme works at a default of 1 mph increments, or any other speed increment I type in if I want to change this. At each speed it looks at the torque, gearing, mass and inertia and drag forces and calculates the acceleration at that point in time. It then works out how long it will take the vehicle to accelerate to the next 1 mph increment (with a few averaging calculations thrown in along the way) and starts again. Each time the speed reaches a gear change point it adds a gearchange interval to the total time. It is perfectly possible to write a system that calculates every 10th of a second or some similar time interval instead. The finer the increments the more accurate the programme will be but the longer the calculation time of course. I have examined this in some detail over the years by trying smaller increments (say 0.1 mph) or larger ones. 1 mph increments turned out to be so accurate anyway that it was pointless doing more detailed calculations in my own programme but if I really want to home in on a specific speed range then I can change the computation interval to anything I like.

I do believe that speed increments are better than time increments though. If you use a fixed time increment then you get a very big change in speed per unit time as the car leaves the line and then at high speed hardly anything happens. A fast car will get to 30 mph in under 2 seconds but might take 10 seconds to go from 149 mph to 150 mph as it reaches its maximum speed. Using 1 mph speed increments means you devote the same amount of computation accuracy to every part of the performance curve.

Assuming there are no actual computational errors then the accuracy of a programme depends on the accuracy of the data. Physics dictates that if the mass and forces are accurately known then the acceleration is a given. Many of the inputs can be known with absolute certainty such as gearing and tyre size. Vehicle mass can be measured to within a fraction of 1% on digital scales. Aerodynamic and rolling drag data should be valid to within a few %. Rotational inertia estimates might be only within 10% or 20% of true but they are such a tiny part of the overall picture that it doesn't matter too much. After 10 years and thousands of simulations I believe my own programme can either calculate the acceleration of a vehicle with known power output or the power of a vehicle with known acceleration to within a couple of %. As good as the accuracy of an engine dyno but with the advantage that every factor that determines how the installed engine will really operate is already accounted for.

Several years ago the motoring journalist and engineer David Vizard, who I've known for many years, tested my programme. We were chatting about various stuff on the phone one day and he gave me the 1/4 mile performance and weights, gearing etc of a car he'd just built for his daughter to go shopping in. Not exactly your common or garden shopping car because it was a Camaro with a bloody great tuned V8 engine in it and special drag strip suspension. He challenged me to deduce the horsepower which he knew exactly because the engine had been on his Superflow dyno before it went into the car. After half an hour of juggling with the programme I phoned him back and said 484 bhp gives me a decent match to the strip times so probably within 20 bhp of that at worst. There was complete silence on the other end of the phone for a moment followed by an expletive of some description. It turns out the engine had made exactly 484 bhp. Now I admit that was a bit of a fluke because with such a powerful engine a couple of bhp either way made next to no difference to the strip times and I just got lucky with the number I settled on. It made him stop and think a bit though and he sat down that same day and wrote an article for Fast Car magazine about it which was published the next month. I can't remember exactly when it was though but maybe around 1992 or 1993.

Here's the rub and we find ourselves back to one of my main hobby horses and the subject of much of the discussion in previous articles. The forces that accelerate a vehicle are the net forces reaching the road surface after tyre and transmission power losses. The programme will calculate based on these net forces very accurately but how do we get back to flywheel bhp? Well the answer is we make sensible assumptions based on testing and previous experience. The result of 10 years of this sort of testing is the reason why I say that transmission losses are usually no more than about 15% of the flywheel power. If I use 15% as my estimate then I find that most standard production cars accelerate very much as the programme predicts based on their quoted flywheel bhp. This ties in with simulations where I have had access to both accurate engine dyno data, wheel bhp data and actual measured vehicle performance once the engine was installed. It's also worth restating that major manufacturers like VW and Bosch quote 15% as being representative of true transmission losses. It's only the performance tuning world and rolling road operators in particular that seem to ignore the facts in the quest for inflated and ego soothing power figures.

This is the normal way in which my own programme is designed to be used. I can use it to help with engine development programmes by seeing how different engine specifications will affect the performance of the vehicle. Will a little more top end power at the expense of some mid range power help or hinder overall performance? To aid in this my programme has some extra bells and whistles which got added over the years. It can simulate an actual race track using corner exit speeds and straight lengths to find out whether a real race car will go faster or slower with different engine specs. That's getting a bit complex though to go into just now. It also automatically calculates optimum gearchange points, which turn out to be at different rpms in each gear in most cases. I suspect that state of the art vehicles like F1 cars and top fuel drag cars use this knowledge already. I can also examine the effect of different gear ratios much faster than actually changing the box and testing the car and in this way I can quickly design the perfect gearbox for a given application.

Most people don't actually understand how acceleration and power are related. It's very simple. Assuming that the vehicle is not grip limited then acceleration is directly proportional to peak power. To halve the 0-30 mph time you need double the power. Remember though that top speed is only proportional to the cube root of peak power. Doubling the engine's bhp should give you twice the acceleration off the line but only about 25% higher top speed. Bear this in mind when you are trying to evaluate the performance goodies you bolted on to your engine. If they really did give you 20% more power then the car should accelerate 20% quicker which is a very dramatic difference. If your car hardly feels any faster then it doesn't have much more power regardless of the claims you were told.

This is very handy when a car has been tested at a drag strip or test track and the actual performance is accurately known. I can calculate the true engine power to within a couple of % if I have access to accurate weight and gearing info. If I test a standard production car from a major manufacturer I tend to find that claimed power is very close to the truth. As we go to the minor manufacturers like TVR, Marcos etc a few anomalies start to creep in from time to time. Some of them rather dramatic but that's for a different story. When we get to claimed power from aftermarket tuning firms the whole plot goes to hell in a handbasket. Almost any time a modified car is properly tested at the track I find that the performance is far below what the claimed power ought to predict. Or in other words, the true power is way below the claims. I'm not talking 10% or so here - often the true power is no more than 2/3 of the claimed power or even worse.

In fact the spur to finally get round to writing this article today after years of putting it off was a Westfield I saw mentioned for sale recently (October 2001) in a car forum on the internet. Enough data was given (weight, gearing, Santa Pod test times etc) to enable a full simulation to be carried out. The claimed power was 330 bhp but the acceleration was that of a vehicle with 254 bhp to within a few % uncertainty according to the programme. Still a damn quick car of course and no fault of the owner who was presumably quoting figures he had been given, but nothing like as quick as it should have been if it really did have 330 bhp. This is not at all unusual and quite typical when I examine claimed power figures taken from rolling road tests, tuning magazine articles etc. The absolute worst cases are turbocharged cars - the power claims bear no relation to how the car actually goes in many cases. Every Cosworth out there with a modified chip seems to have 350 bhp claimed for it but it's a safe bet you can knock 25% or more off the claims before you get anywhere near the truth. This is because there are no real limits to how much power a turbocharged car can make so it's hard to know whether the claims are possible or not. With a normally aspirated car you can generally guess the potential power from the valve area, state of tune and the engine size.

The problem of course is that big horsepower claims help sell tuning products but often don't make the car go much faster. Physics, and Newton no doubt if he were still alive, has harsh things to say about this. You can't increase power without making the car faster - so if in fact the car is not faster then the power hasn't gone up - QED. It doesn't matter what the rolling road or the engine builder told you, the proof of the pudding is in the eating, or on the track as the case may be. The standard cop outs for dubious power claims seems to be phrases along the lines of "well the throttle response is much improved" or "the driveability is better" whatever any of that means.

Computer simulations are becoming more commonplace and more accepted. A number of programmes are available on the internet, either to download or to run in a Java applet. I haven't actually looked at any in detail to see how sophisticated they are but there's no doubt that the world is not short of people with decent maths and programming skills and I'm sure many of these programmes are very good. A couple of years ago I came across a web site by a guy called Bowling who had some good car related programmes - maybe it's still out there somewhere. As they become more available then inflated horsepower claims can be put to the lie if the car's performance is tested. In the past it has been very hard to do this. Put the average driver in a 250 bhp car and tell him it's got 350 bhp and he isn't going to know any better just from how fast it goes. It's still a damn quick car and probably faster than anything else he has ever been in so he has nothing to compare it with. Even professional test drivers aren't going to be able to estimate power with any great accuracy, or at least with enough accuracy to really dispute a power claim in print. Test the actual performance of the car and run the data through a decent simulation programme though and the power claim anomalies start to become quantifiable for anyone who can type the numbers in.

No - my own programme isn't available anywhere. Nor will it probably ever be. I wrote it for my own use and for my own development work.

No - I can't help you with how to write your own programme but good luck if you try. I just don't have the time to enter into detailed email correspondence. In any case you'll learn more about vehicle dynamics in the search for the information than you will by someone just handing it all to you on a plate. This and the previous articles should take you a good chunk of the way though.