When I started out writing these technical articles there was some
sort of overall plan that the pieces would fit together in the end to form a
picture of how maths and physics operate to determine how engines and vehicles
work. The aim was to try and dispel at least some of the myth and bullshit that
pervades the tuning industry in the attempt to make people buy tuning parts
that aren't properly designed and don't work. Fundamental principles are very
powerful tools to help us decide what is and what is not possible.
Unfortunately most people don't have the maths or education to apply these
tools. Hopefully this website will have helped those who want to learn to
appreciate some of those fundamental principles. One of my biggest hobby horses
is the supposed flywheel power figures that tuning firms and magazines attempt
to derive from wheel bhp figures taken from rolling road tests. In the main
these are vastly overinflated. Many people seem to think that as much as 30% or
more of the flywheel power is lost in the transmission. A simple reposte to
that is that gearboxes would melt if they soaked up so much energy but there
are more powerful arguments to use.
My own figures for transmission losses have been stated in
previous articles but to recap they are usually no more than 15% of the
flywheel power for FWD vehicles and no more than 17% for RWD ones. A good guide
is to deduct 10% of the flywheel figure plus another 10 bhp for FWD and 12%
plus 10 bhp for RWD. If you are starting from a wheel bhp figure then you have
to apply those equations in reverse - add 10 bhp then divide by 0.9 for FWD or
0.88 for RWD to get back to a flywheel figure. Those figures were not just
plucked out of thin air. They represent the culmination of many years of
research and testing combined with the views of reputable companies like Bosch
and VW.
There is however a final way of estimating what transmission
losses really are based on the most accurate dyno in the world - the car
itself. Physics tells us that it takes a certain amount of energy to push a
given shape through the air at a given speed. The maths behind this is not open
to debate. It's part of the basic physics that determines how the universe
operates. The article on how top speed and engine power are related goes into
this in some detail. The power available to force a car to its top speed is
obviously the net power at the wheels after all tyre and transmission losses.
If we can work out this net power and we also know the flywheel bhp figure then
the transmission losses must be the difference between the two. To work out the
power requirements of a car based on its top speed we need to know its drag
coefficient and its rolling resistance. For light vehicles, like passenger
cars, the rolling resistance is about 0.013 x the vehicle mass. Drag
coefficients are measured and published by the manufacturers. If we take a
couple of examples we can see how this required power ties in with the engine's
flywheel bhp. The equations are explained in more detail in the previous
article so read that first if you haven't already done so.
The 1.8 Vauxhall Astra GTE (new shape from 1985 on) has a frontal
area of 20.5 sq feet and a Cd of 0.31. With two people and some test equipment
on board (which is how most reputable magazines do their tests) the car weighs
about 2460 lbs. The engine is rated at 115PS (about 113 bhp) and the tested top
speed is about 123 mph. let's see how much net power is required to achieve
that speed.
Rolling resistance power is 0.013 x 2460 x 123 / 375 = 10.5 bhp
Air resistance power = 20.5 x 0.31 x 0.00256 x 123 cubed / 375 =
80.7 bhp
Total bhp at the wheels must be about 91.2 bhp to achieve that
speed. If we apply my formula for FWD cars to the quoted flywheel power we get
(113 x 0.9) - 10 = 91.7 bhp at the wheels. Hmmm - so you gonna step outside and
fight me about 0.5 bhp or is this starting to make some sort of sense?
Let's try a more powerful car.
The 2WD Sierra Cosworth was rated at 205 PS (about 202 bhp). Top
speed was in the 145 mpg region according to most magazines. Test weight with 2
people and 50 lbs of equipment on board is around 3060 lbs. Frontal area is 21
sq feet and Cd is 0.35.
Rolling resistance power is 0.013 x 3060 x 145 / 375 = 15.4 bhp
Air resistance power is 21 x 0.35 x 0.00256 x 145 cubed / 375 =
153 bhp
Total net power required is 168.4 bhp. Apply the RWD formula to
202 bhp and we get (202 x 0.88) - 10 = 167.8 bhp.
The conclusion here is pretty obvious. If transmission losses were
as high as 30% then there just wouldn't be enough power left at the wheels to
achieve the top speeds that the cars actually show. The Cosworth would only
have 141 bhp at the wheels if this were the case and its top speed would
therefore only be around 136 mph. You can work that out for yourself by
applying the formulae above. The Vauxhall would only have 79 bhp at the wheels
and be capable of around 117 mph.
Of course every magazine test achieves a slightly different top
speed and published drag coefficients vary a bit depending on the source. If
you carefully select your data depending on what you are trying to prove you
can show just about anything. But if you run enough of these calculations and
also factor in the acceleration from computer simulations you start over the
years to build up a picture of how things really work. The conclusion is that
transmission losses are much lower than commonly quoted. The only reason to
apply big transmission loss percentages is to flatter the supposed flywheel
power outputs from poor tuning work.
Ask any tuning firm which applies these big transmission losses
why they do so and about the best you are going to get in reply is "that's
what we've always done" or "we read it in a book somewhere
once". Hopefully a proper scientific argument like the above will be a bit
more convincing. You don't even have to take my own word for it. All the
equations I use are part of fundamental physics and commonly quoted. The book
"Internal Combustion Engine Fundamentals" by J.B.Heywood is a good source
and he is the professor of automotive engineering at MIT so dispute him at your
peril.