When the flywheel of a car is lightened it can have a great effect
on acceleration - much more than just the weight saving as a proportion of the
total vehicle weight would account for. This is because rotating components
store rotational energy as well as having to be accelerated in a linear
direction along with the rest of the car's mass. The faster a component
rotates, the greater the amount of rotational kinetic energy that ends up being
stored in it. The engine turns potential energy from fuel into kinetic energy
of motion when it accelerates a vehicle. Any energy that ends up being stored
in rotating components is not available to accelerate the car in a linear
direction - so reducing the mass (or more properly the "moment of
inertia") of these components leaves more of the engine's output to
accelerate the car. It can be useful to know how much weight we would need to
remove from the chassis to equate to removing a given amount of weight from the
flywheel (or any other rotating component). There is more than one way of
solving this equation - we can work out the torque and forces acting on the
various components and hence calculate the accelerations involved - also we can
solve it by considering the kinetic energy of the system. The latter approach
is simpler to explain so this is the one shown below.
Let's imagine we take two identical cars - to car A we add 1 Kg of
mass to the circumference of the flywheel at radius "r" from the
centre. To car B we add exactly the right amount of mass to the chassis so that
both cars continue to accelerate at the same rate. If we accelerate both cars
for the same amount of time they will end up at the same speed and will have
absorbed the same amount of kinetic energy from the engine. In other words, the
additional 1 Kg in the flywheel of car A will have stored the same amount of
kinetic energy as the additional M Kg of mass in the chassis of car B. To solve
the problem of the size of M we need to use the following definitions:
V - the speed of either car after the period of acceleration
R - the tyre radius
G - the total gearing (i.e. the number of engine revolutions for each tyre
revolution)
r - the flywheel radius (i.e. the radius at which the extra mass has been added
to car A)
M - the amount of mass added to the chassis of car B
Kinetic energy is proportional to ½mv² - the kinetic energy stored
in the extra chassis mass in car B is therefore ½MV².
The extra 1 Kg of flywheel mass in car A stores linear kinetic
energy in the same way as if it were just part of the chassis. After all, every
part of the car is travelling at V m/s - so it stores linear kinetic energy of
½ x 1 x V² = ½V².
To find out how much rotational kinetic energy the 1 Kg stores, we
need to know the speed the flywheel circumference is travelling at. The car is
travelling at the same speed as the circumference of the tyre (assuming no tyre
slip of course). We know that for every revolution of the tyre, the flywheel
makes G revolutions. However the flywheel is a different size to the tyre - so
the speed of the circumference of the flywheel is VGr/R. The rotational kinetic
energy is therefore ½(VGr/R)².
Now we can put the whole equation together - the extra kinetic
energy in the chassis of car B = the sum of the linear and rotational kinetic
energies in the 1 Kg of flywheel mass of car A - therefore:
½MV² = ½V² + ½(VGr/R)² =>
½MV² = ½V² + ½V²(Gr/R)² => divide both sides by ½V² to arrive
at the final equation:
That wasn't so bad then - we managed to avoid using true
rotational dynamics involving radians and moments of inertia by considering the
actual speed of the flywheel circumference. This did of course involve assuming
that all the mass added or removed from the flywheel was at the same radius
from the centre. In the real world that is not going to be the case so we need
to use moments of inertia rather than mass to solve the equation. The simple
equation above is useful though in getting an idea of the relative effect of
lightening components provided we have a good idea of the average radius that
the metal is removed from. It can be seen that gearing is an important factor
in this equation. The higher the gearing the greater the effect of reducing
weight - so for a real car the effect is large in 1st gear and progressively
less important in the higher gears. We can also hopefully see that when r is
larger, so is the effective chassis weight M. So removing mass from the outside
of the flywheel is more effective than removing it from nearer the centre.
It might at first look as though tyre diameter is important but of
course it isn't for a real car - if tyre size was to change then so would
gearing have to if overall mph per thousand rpm were to stay the same - the two
factors would then cancel out again.
To show the sort of numbers that a real car might have, I did some
calculations based on a car with average gear ratios and tyre sizes - the table
below shows the number of Kg of mass that would have to be removed from the
chassis to equate to 1 Kg removed from the O/D of the flywheel at a radius of 5
inches.
|
GEAR |
MASS KG |
|
1 |
39 |
|
2 |
12 |
|
3 |
6 |
|
4 |
4 |
|
5 |
3 |
So in first and second gear this is a pretty important effect - I
built an engine recently and managed to remove nearly 3 Kg from the outside of
the standard flywheel - so that would be equivalent to lightening the car by
over 100 Kg in 1st gear - not to be sneezed at in terms of acceleration from
rest. With special steel or aluminium flywheels even more "moment of
inertia" can be saved. The recent trend in racing engines to using very
small and light paddle clutches and flywheels is therefore more effective in
terms of the overall performance of the vehicle than it might first appear.
There's a final consequence of the "flywheel effect"
being dependent on gearing. Small highly tuned, high revving engines need to
run much higher (numerically) gearing than large, low tuned engines. This means
that the effect can be very pronounced on them. Bike engines are a good case in
point, especially as they are now starting to be used in cars so much. A 100
bhp bike engine might only be 600cc and rev to 12,000 rpm. A 100 bhp car engine
might be 2 litres and rev to 5,500 rpm. Put the bike engine in a car and you'll
need to run a final drive ratio twice as high as for the car engine. As the
flywheel effect is proportional to the square of gearing, it will be 4 times as
high for the bike engine. You could therefore be talking about 1kg off the
flywheel being equivalent to 160kg off the weight of the car. That's why bike
engines have such small multiplate clutches to keep the moment of inertia down.
On the other side of the coin, it's not worth spending much money lightening
the flywheel of a 7 litre Chevy engine revving to under 5,000 and geared for 60
mph in first as the vehicle will be very insensitive to the reduction in
weight.
If you are going to get your standard cast iron road car flywheel
lightened then be sure to take it to a proper vehicle engineer and not just
your local machine shop. Take off too much material and it might be weakened so
much that it explodes in use. Given that flywheels (at least in rear wheel drive
cars) tend to be situated about level with your feet, it isn't worth the extra
acceleration if you lose both feet when the ring gear comes out through the
side of the transmission tunnel like a buzz saw at 7,000 rpm. There are plenty
of ex racing drivers hobbling about on crutches who'll tell you that this can
and does happen. On FWD cars the effects can even more unpleasant - a flywheel
entering the cabin can give you a split personality starting from just below
the waist that will put quite a crimp in your day. Also when you remove any
weight from the flywheel it will need re-balancing again properly. We'll be
happy to do the job for you if you don't know of an experienced engineering
shop.
All other components which rotate absorb energy in addition to
them having to be accelerated linearly along with the chassis. Components which
rotate at engine speed like flywheels are the most cost effective ones to
lighten in terms of their equivalent chassis mass but it pays not to overlook
the mass of any rotating component. The next major category is items which
rotate at wheel speed - wheels, tyres, discs etc. These don't rotate as fast as
engine components but they can be very heavy. The average car wheel and tyre
weigh about 45 lbs together. A good rule of thumb is that in addition to its
own normal weight a wheel speed item adds the equivalent of an extra 3/4 of its
mass to the effective chassis mass and this figure is not dependent on gearing
so it stays a constant at all times. It's a smaller effect than the flywheel
effect which can be many times its own mass in first gear but still important.
Let's say you fit wide wheels and tyres to your car. If each corner weighs an
extra 10 lbs more than the standard items then the effective increase in
chassis mass is 40 lbs for the direct weight plus another 30 lbs being 3/4 of
the direct mass - a total of 70 lbs. On a light car like a Westfield or
hillclimb single seater this could be between 5% and 7% of the effective total
car weight. Equivalent to knocking the same percentage off the engine's power
in acceleration terms. That's why F1 and other high tech series designers
strive so hard to reduce weight in this area and use magnesium instead of
aluminium for wheels and the thinnest possible carcasses for tyres. It also
reduces unsprung weight of course which helps the suspension and handling. Even
on a 1 ton road car the effect of heavy wheels and tyres can be noticeable in
terms of reduced acceleration. Wider tyres also absorb a bit more power in
friction which doesn't help either if the engine is on the small side.
The other few rotating items, gearbox internals, camshafts etc are
generally of small diameter and not worth lightening because of their
consequent low inertia. One thing I can promise you is that the current fad for
anodised aluminium cam pulleys which then usually get hidden behind a cover
anyway won't make a scrap of difference to your engine because of the few grams
weight they save. They may well wear out and cost you your entire engine if the
teeth strip off the belt though. Aluminium is not really the material for gears
and sprockets but when did fashion and common sense ever go together?