Drag Forces?

Question

i have the drag formula:

F = -0.5 * 1.293 * speed^2 * frontal_area * drag_coeff

My car has a frontal_area no less than 1.5m2 and drag_coeff no less than 0.2

Running the formula through various speeds I get :

30kph = 8.333m/sec - Drag = 13.468

50kph = 13.888m/sec - Drag = 37.413

80kph = 22.222m/sec - Drag = 95.777

120kph = 33.333m/sec - Drag = 215.5

I am assuming the Drag force is in Newton-metres, but this doesnt make sense. My car's engine only produced 145NM/torque when it was brand-new (which it definately isnt now) so why can it exceed 120kph?

Do I need to calculate further to work this out?

Answer 1

You can but, maybe you just broke in your engine.

Answer 2

I think you are confusing the term for the torque from the motor. Notice that it is in Newton Meters, not Newtons as the drag term is. This means that there is something wrong in your analysis and that you cannot make a conclusion from it.

What you need to consider is the thrust force that torque from the motor produces at the wheels. This Force is what will couteract the drag force for constant speed, or exceed to produce acceleration. So the first thing you would want is the engine speed at which your car is running at these various speeds. we will call this "N" in RPM. Now if you have the engine torque curve you can also read the maximum torque your engine can put out at this running speed, we will call this "Tmax". You also need to know the diameter of the wheels, call this "Dw"

Now you can find the rotational speed of the wheel as "Nw" with "V" the speed of the car.

Nw = 2*(V/Dw)*9.55   - 9.55 is conversion from rad/s to RPM

So now you have the rotational speed of the wheels and you know the rotational speed of the motor, so you can calculate your gear ratio as:

G = N/Nw                 - this is dimensionless

Now you can determine the torque at the wheels using your gear ratio and the max torque your engine can put out at the running speed.

Tw = Tmax*G             - units of Nm again

Now finally the force at the wheels can be found as:

F = 2*Tw/Dw

Now if this is greater than the drag force you can accelerate. For example if you have:

N = 3000 RPM     - speed of engine at 120km/h

Tmax = 145 Nm   - assuming max torque occurs at 3000RPM

Dw = 0.508m       - 17in rims and a few inches of tire

V = 33.333m/s     - 120 km/h

Then:

Nw = 2*(V/Dw)*9.55 = 1253 RPM

G = N/Nw = 2.394

Tw = Tmax*G = 347.09 Nm

F = 2*Tw/Dw = 1366.5 N

So even though your drag force is 215N as you calculated the thrust force the wheels can provide would be maximum 1366N. The difference being 1151N so if your car weighed 1500kg the acceleration can be found as:

a = (F-D)/m = 0.767 m/s^2

So you can still accelerate at a reasonable rate at 120km/h