Aerodynamics, friction, power and performance.

 

Author Bob Carter

 

How much electrical power do we have?

 

The GreenPower race rules allow us 4 specific batteries for a 4 hour race, to be used 2 at a time in the car. Each “battery full” of electricity gives us a specific amount of energy, and this is detailed in the battery’s specification. We are using “75 amp hour” batteries.

 

So in theory they should give us 75 amps for an hour or 37.5 amps for 2 hours. However, it turns out that the batteries only give out this much power if you discharge them really slowly.

 

We discharge them quite fast during a race!

 

At the 2hr discharge rate we can only get 50 Amp hours of charge out of the batteries, therefore we work with an average battery current of 25Amps. 

 

From your science lessons you may remember that

 

          Electrical Power = Volts x Amps = 24V x 25A = 600Watts

 

That is the power of 6 ordinary light bulbs, or a big Hoover, or one fifth of an electric kettle.

 

What happens to that power in a race?

 

Of the power that the batteries give us:

 

1)    some is lost in the speed controller as heat

2)    some is lost in the motor as heat

 

What is left is the mechanical power that is actually used to push the car along: -

 

3)    some is used to overcome friction

4)    some is used to push the car through the air

5)    some is wasted by using the brakes to slow down

 

We have figures for many of these.

 

1)    the speed controller wastes 4% of the power, leaving 576W

2)    Electrically we can think of the motor as having an effective resistance, so any electric current in the motor will heat the resistance up. The GreenPower motor resistance is 0.185ohms.

 

Now:

          Volts = Amps x Resistance

And

          Power = Volts x Amps

So

          Power = Amps x Resistance x Amps = 25 x 0.185 x 25 = 115.6Watts

 

Finally we know the mechanical power available to the car.

 

It is 460.4Watts

 

We also know that the motor is going to get hot – it has at least 115 Watts of heat in it – that’s more than a 100W light bulb! The speed controller will also get warm; it has 24W of heat in it. That’s why these parts of ‘Brian’ have cooling fans. Actually the motor also heats up due to mechanical friction losses.

 

So how fast can we go?

 

The mechanical power is used to overcome the 2 sources of drag; friction and aerodynamic drag. Unfortunately we do not have the technology to directly measure these factors at race speed in our cars, so we do not directly know their aerodynamic properties or dynamic friction. However, we do have the complete data log from Brian at the Goodwood final, and can separate these factors via the logged data.

 

Aerodynamics and friction have very different characteristics. Friction force is the same at all speeds, whereas aerodynamic drag force gets much bigger as speed increases, being proportional to speed2

 

So the force needed to push the car forward = F + A v2

                    (F is friction force and A v2 is aerodynamic drag force)

 

Now, because

                    Power = force x speed

 

We get:

                    Power needed to push the car forward = F v + A v3

 

Let’s see if we can see that shape in the data log from the final: -

 

Here is a graph showing each of the 44 laps, car speed vs. battery power.

 

The blue dots are real logged data from each lap of the final. The purple dots are the function

          Power = 10.1 x speed + 0.00503 x speed3

(we have chosen coefficients for F and A to best fit the measured data)

 

So to get back to the question, how fast can we go? If we include the fact that the battery voltage reduces as the batteries go flat, and that Brian has slow pitstops; the formula above gives Brian an average speed of 27.9mph, covering 105.2 miles in 3.77 running hrs. – and sure enough we achieved 105.6miles.

 

What about the new car? This has the same drive mechanics as Brian so we would expect its friction to be the same. Its frontal area, on the other hand, has reduced from 0.63m2 to 0.23m2, so its aerodynamic factor should reduce by the same ratio. The same analysis (including much faster pit stops) gives Raptor an average speed of 34.3mph – a projected distance of nearly 135 miles in 3.95hrs. Will it get that far? Time will tell…. It was designed to win (so was Brian, but we now have better data!).

 

Note that other builders (e.g. PortaPrompt & TSR) have suggested that cars’ power losses were almost all aerodynamic and that friction losses were negligible. Our data logs suggest otherwise, and that friction losses (much of which is within the motor itself) are nearly as large.

 

The component of friction due to the motor will actually reduce at higher speed when a higher gear ratio is selected.