Model Forum / Radio Controlled / Land Models / January 2004

Since physics doesn't scale as well as dimensions do, why don't you set up
your track to test the limits of your vehicle as is?  You'll go bonkers
trying to figure out the power/weight ratios (greater than that of an F1
racer) vs scale speed vs traction coefficient.  If you want the satisfaction
of beating someone else, look into organized racing.

Unlikely.  Remember that gravity doesn't scale, and neither does
coefficient of friction ('cos it's a coefficient, natch!) so acceleration
also tends to remain the same.  I once spent a couple of hours lying awake
trying to figure this out (sad, I know ;-) and came to the conclusion that
you need to think of *time* being scaled, by the square root of the scale
factor.  I've mentioned this here before, so try Google.  (This is why
videos of model cars look "wrong".)

So, if you scale the track down by 10 (lengths are always by the scale
factor) and then figure the speed by 3.16, it might just work.

Of course, the problem is likely to be that the track is far too narrow in
the sections where you're looking across it...

Actually, power-to-weight is about right to a little bit low.  Depending
exactly how much horsepower you think a hot modified produces (150-200 W?)
my 1.6 kg buggy has 120-170 bhp/tonne, compared to a WRC car at maybe 300
bhp and 1.5 t => 200 bhp/tonne.  IMO a 4WD buggy moves much like a WRC or
Rallycross (~500 bhp?) car, and the difference could be accounted for by
the better low-end torque of an electric motor.

Jonny

The 1:10 scale is for length.  That is 1:100 for area, and 1:1000 for
volume.

Now, speed = distance/time, and as time is the same in RC world as real
world, then speed scales as a factor of 10 too.

So, if you want your 1:10 scale buggy to look as if it's going 100mph, you
drive it at 10mph.

What about top speed?  Top speed is when forward force = drag forces.  So
top speed is proportional to the cube root of power, which is 1:10, so the
top speed should be 10 times less.  My car has a top speed of 40mph, this is
certainly closer to 10 times less than a real car (with 1000hp!) than it is
to 100 times or 1000 times less.

Power/weight ratio is going to be roughly the same.  Power roughly depends
on capacity of the engine, which is a volume factor (ie 1:1000), but weight
also depends on volume, so they cancel out.  My car generates about 1HP and
weighs about 2.5kg, so that's 400hp/tonne, about right for a racing car.

Now acceleration.  There are two situations, one is limited by tyre/road
friction, the other is limited by engine power.  Tyre/road friction is equal
to normal reaction force times coefficient of friction.  Normal reaction
force is related to weight, and hence volume, so will be 1000 times less in
your R/C car.  Coefficient of friction will be the same, so the acceleration
*force* will be 1000 times less.  But the mass is also 1000 times less, so
the absolute acceleration will be of similar magnitude to real life.  The
same goes for acceleration limited by engine power: the engine power is 1000
times less, but the weight is too.

This is what makes them look unrealisitically fast, the acceleration
*should* be 10 times less for it to look right on video.  If you could make
someone believe your 1:10 car was full-size on video, it would appear to do
0-60 in under a second (0-6mph actually, but it looks like 0-60mph).

The same applies to the cornering accelerations, these are also 10 times
higher than they 'should' be.  This makes the maximum cornering speeds about
3 times faster than they 'should' be (lateral acceleration = speed^2 /
corner radius)

You could also work out the resonant frequency of the suspension and stuff
like that too and see how that scales, this probably makes them look 'wrong'
too.

It's all about units, and it's never going to look right.

Scott