So I have a free axle (i.e. just an axle, no car) with two wheels (one at either end), but the wheels are not the same radius.

If I were to push this axle along the ground, it would travel in a circle. Does anyone know how I might determine the radius of this circle?

For bonus points, if there are now two such axles connected at a fixed distance ahead of one another (hmm, like a car!), how would this effect the radius?

The radius of the circle is the lenght of the axle?

r_b = radius of the big wheel
r_s = radius of the small wheel (or r_i)
l_w = distance between the wheels
r_c = distance between inner wheel and corner middle point

=>
u_b = 2*pi*r_b
u_i = 2*pi*r_i

r_c = ( ( l_w * u_b) / (u_b - u_i) ) - l_w

If I'm not mistaken. Sadly my scanner ain't working so there is no drawing.

EIDT: Scanner working, badly drawed picture attached...

Quote from three_jump :

Some formulas that go way above my head

Did VOlker Strycek teach you that?

Quote from speedway :

edit: Dreisprung, i havent seen such a horrible documentation in years

fffuuu, it's exactly how it's supposed to be.

Quote from Bob Smith :

So I have a free axle (i.e. just an axle, no car) with two wheels (one at either end), but the wheels are not the same radius.

If I were to push this axle along the ground, it would travel in a circle. Does anyone know how I might determine the radius of this circle?

For bonus points, if there are now two such axles connected at a fixed distance ahead of one another (hmm, like a car!), how would this effect the radius?

coding an oval sim are we? naughty naughty

first on is easy
just find the crossing point of the lines through the contact patch and through the axle... that should be your circle centre
think of the axle as part of a cone which naturally behaves the same as the whole cone which (not considering slip) should roll around its tip
which if im not mistaken is what 3j said there in a needlessly complicated fashion

second one is incredibly complicated as you have to deal with slip ratios slip angles and all that nonsense

Quote from three_jump :

r_b = radius of the big wheel
r_s = radius of the small wheel (or r_i)
l_w = distance between the wheels
r_c = distance between inner wheel and corner middle point

=>
u_b = 2*pi*r_b
u_i = 2*pi*r_i

r_c = ( ( l_w * u_b) / (u_b - u_i) ) - l_w

If I'm not mistaken. Sadly my scanner ain't working so there is no drawing.

EIDT: Scanner working, badly drawed picture attached...

A bit of offtopic..
Can you give me your brain? I suck at maths and am very jealous of ppl like you.

Don't be. If you suck at maths that may indicate that you are a happier person! Yay for you!
(In reference to this)

Vain

Quote from three_jump :

r_b = radius of the big wheel
r_s = radius of the small wheel (or r_i)
l_w = distance between the wheels
r_c = distance between inner wheel and corner middle point

=>
u_b = 2*pi*r_b
u_i = 2*pi*r_i

r_c = ( ( l_w * u_b) / (u_b - u_i) ) - l_w

If I'm not mistaken. Sadly my scanner ain't working so there is no drawing.

EIDT: Scanner working, badly drawed picture attached...

You missed some points in practical view there though.

The axle will just behave like a cone.

the Contact patches/parts of the tyres will be the points to draw the line through.

So the radius can change depending on corners, because the contact patch of the tyre will not always be in the center of the tyre.

The contact point is the vital issue here, but on a straight line without steering you should be right.
I think I should be right, but if I'm not, blame me!

As far as I understood the original post the question was about a simple solid axle with 2 different wheel sizes. If you move that axle at very slow speeds (stationary) you should be able to ignore the friction / slip issues. And there was nothing said about steering

That's true, I thought about that after I posted my post which seemed very smart.

Quote from Shotglass :

just find the crossing point of the lines through the contact patch and through the axle...

Aha, yes, that makes sense, easier than I first thought when you think about it that way. I should be able to work that out in the morning and hopefully looking at my maths will make three jump's post a little more clearer. Thanks.

Quote from Shotglass :

second one is incredibly complicated as you have to deal with slip ratios slip angles and all that nonsense

Bah. Particularly when the wheels may not be free to rotate at different speeds. Maybe I can bodge something up for a reasonable estimation of the bonus question.

Quote from speedway :

Lets say the radius for one axle was 20m, would you still be able to keep that radius if two axles were 50m apart?

Of course not. Clearly increasing wheelbase will increase the radius the vehicle will try and turn in.

Quote from Bob Smith :

Particularly when the wheels may not be free to rotate at different speeds.

isnt that the whole point? if you put the wheels loosely on the axle or axles id expect the whole thing to just roll straight ahead

Ah but the difference in radii causes the wheels to camber, and you get camber thrust, and they won't cancel out.

we shall perform a experiment!

lets get the most expensive things we can buy for this, this includes 10 ferrari enzo's, 7 bugatti veyrons, and 8-10 pizzas

lets get started in our important work

Quote from Shotglass :

isnt that the whole point? if you put the wheels loosely on the axle or axles id expect the whole thing to just roll straight ahead

Having tested this morning, this was more important that I at first though. More importantly though, this did manage to get me thinking and I've solved my problem now, and I didn't even need to know the radius in the end.

lovely jobly.

I have officially fried my brain and killed brain cells due to information overload reading and trying to understand this thread!