How many rpm to reach 400kph...

[tomislavp4]

Ok, you have a wheel with radius of 21in and it´s 335mm wide. How many rpm should the wheel make to reach 400kph?

I had the formula but I cant find it... hope u can help

[pyry]

do you mean how many rpm the wheel is spinning at at 400kph? how many rpm the wheel should make to reach 400kph depends on the engine and car.

[tomislavp4]

Lets just say that the wheel is roling alone and there is no car. So the wheel goes 400kph how many rpm it has?

[Saribro]

400kph = 6666m/min
21 inch = 0.53 meters -> circumference = 3.14*0.53 = 1.66m

6666/1.66 ~= 4000RPM for the wheel to reach 400kph.

[Ciro Pabón]

No, pyry, tomislav asks for the rpm of the wheel, not the rpms of the engine.

It depends only on the diameter of the wheel. You say a wheel with 21 inches radius, wich is around 53.3 cm.

So, the circunference of the wheel is 2*Pi*53.3 = 335.1 cm, not Pi*r as saribro used (tomislav gave the radius, not the diameter). Each turn of the wheel moves you a little over 3 meters.

Now, if you move at 400 kilometers in one hour, you have to move yourself 400/60 = 6.66 Km in a minute, right?

The number of turns per minute is 6.66 Km / 3.35 meters = 1990 turns.

So, the answer is 1990 rpm, give or take a few.

The wheel will become larger at high rpm because of the centrifugal force, but that effect is relatively slight and depends on the stiffness of the tyres. This will make a greater circumference, longer distance in one turn and slightly less rpms.

Just for fun, at that speed, the edge of the tire moves at 6.66 Km/60 seconds = 111 meters per second.

The radius is 0.53 meters, as we said before. The centrifugal acceleration is the speed squared divided by the twice the radius. That is (111 m/s)^2 / (2*0.53 m) = 11623 m/s2. This is like 1180 G's!

Am I wrong in that last one? Over 1000 G's? Anyway, you better use high speed tyres on your first attempt...

[pyry]

you didnt take into account the flexing and deformation of the tyre at those speeds. the circumference grows to some extent.

[Ciro Pabón]

That's what I said, pyry, unless you're answering saribro's post. That should be easy to calculate if you know the stiffness modulus of the rubber, given the 1180 Gs I assume. You also need to know how "high" is the tyre, that is, the distance from the edge of the rim to the edge of the tire. Finally, you need the weight of the tire. You convert the centripetal acceleration to Newtons, using the unit weight of the tire (per length of thread), calculate the radial deformation dividing the resulting force by the modulus of elasticity and the height of the tire and add that result to the diameter of the tire, if I am right.

[tomislavp4]

Thanks guys, u are the best

[Saribro]

So, the circunference of the wheel is 2*Pi*53.3 = 335.1 cm, not Pi*r as saribro used

That's because I assumed 21inch diameter instead of radius, it seems to me a 1m+ diameter wheel is kinda nutty.

[EDIT]
Silly me, I totally missed the mentioning of "radius" in the original post :).

[tomislavp4]

Damn how stupid I am...
I meant diameter not radius

[Saribro]

Damn how stupid I am... :oops:
I meant diameter not radius ](*,) ](*,) ](*,) ](*,)

Huray, score 1 for Saribro :D

[RACKITUP]

Just for fun, at that speed, the edge of the tire moves at 6.66 Km/60 seconds = 111 meters per second.

The radius is 0.53 meters, as we said before. The centrifugal acceleration is the speed squared divided by the twice the radius. That is (111 m/s)^2 / (2*0.53 m) = 11623 m/s2. This is like 1180 G's!

Am I wrong in that last one? Over 1000 G's? Anyway, you better use high speed tyres on your first attempt...

centrafugal accel, a=(V^2)/(2*r)???

I "think" it's a=(V^2)/(r) and with thr OP's corrected radius, its in the region of 4730g's, not that much considering other areas of the car that undergo compressional/tension forces, such as the pistons

[pyry]

ciro, in my first post i was being sarcastic, as the question was "how many rpms to reach 400kph" which directly translated means how many revolutions must the wheel turn before it reaches 400kph, ad that DOES depend on the car and engine and yes, you post wasnt there yet when i wrote my second post