Slip Angle Calculation

[HJsimpson]

Hi,

I'm trying to calculate slip angles for a vehicle simulation I'm creating, and I'm not confident of my results (this is not my field of expertise, but I'm trying). My understanding is that the sign of the front & rear slip angles should be negative for a RH turn, yet my rear slip angles are positive. I've pared the calculations down to a basic bicycle model, but I can't find my error. A picture of my workings is attached.

Many thanks for any thoughts or comments provided.

 

[GregLocock]

you have at least one error confusing radians and degrees

Cheers

Greg Locock


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[HJsimpson]

Hi Greg,

Thanks for the reply. At the risk of sounding like an idiot; I don't think I do?

I understand that I have quoted some values in radians and others in degrees, which can be a little confusing. Also, the stated equations don't have unit conversions stated within them, although the formulas within the cells do (I figured this didn't need to be stated).

I've just gone through and re-calculated it from scratch, and I received the same answers. I'm happy to concede an error in this regard, but I just can't see what it is.

 

[GregLocock]

Oh I was going by the equations you put up since that was all I had to go by unless you were intending I should replicate your work exactly.



Cheers

Greg Locock


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[cibachrome]

For a steady state right turn (positive delta), Beta is negative. Try to keep in mind that understeer is a derivative, not just a simple difference. While it may work in this case, as you add nonlinear terms, your results will be wrong, you may go to jail, and you may be forced to push a ball uphill forever, only to have it roll backward on your toes after 5:00 p.m.

 

[HJsimpson]

Greg,

I'm not intending for anyone to replicate my work. Let me put it this way:

* I haven't been formally taught vehicle dynamics.
* I've read four textbooks on this, and they seem to contradict each other at points, which is a touch confusing.
* I haven't got anyone to ask personally, plus my local universities don't teach vehicle dynamics.
* This is a small part of a much bigger picture for me. If there's an error here, it can compound into a real mess for me later on.
* Basically, I'm running out of road trying to understand this. Eng-tips was pretty much my last shot.

I was just hoping someone could look at my calculations and say "hey, your understeer gradient doesn't look sensible" or "in some circumstances the slip angle signs can be opposite" or... something.

I suspect I've come across like a student wanting somebody else to solve my homework problem. Perhaps I've worded by thread poorly.

If anyone can offer assistance, I would appreciate it.

 

[HJsimpson]

Cibachrome,

I hadn't seen your post when I replied to Greg earlier. Thanks for the response - that's the kind of reply I was hoping for. I'll have to do some more reading on Beta and the understeer gradient.

Thank you!

 

[patprimmer]

HJ

This is not my area so I am as confused as you on this subject, but as I read your OP, I wondered about the things you just addressed. I suggest that your wording put some potentially very helpful people offside.

Your later explanation might turn that around.

Regards
Pat
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[GregLocock]

If you post your spreadsheet rather than a screenshot then I'll take a look at it.

Sign conventions are a mess (in general, that's why every serious VD textbook has a chapter on coordinate systems), but in a 1.5g turn the chances are very high that both axles will have the same sign for the slip angle.

Cheers

Greg Locock


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[cibachrome]

BTW: My first comment was for the speed you indicated. Sideslip can be positive, in your case when speed is below 34.5 km/hr.

Otherwise, it has the following linear range properties:
The sideslip per g would be -2.41 deg/g
The front cornering compliance would be 4.64 deg/g
The rear cornering compliance would be 2.72 deg/g
(for an understeer of 1.92 deg/g)

The Tangent Speed (speed at which sideslip changes sign) is about 34.5 km/hr and you would be pulling about .23g lateral in a constant radius test when that happens. (These are is my units and industry vernacular).

If you put a 20:1 overall steering ratio in this 'vehicle', you'd have a sporty gain of about 1.87 g/100 deg swa which is a bit high for my liking but cars like this are out there.

Given these results, I could name a brand of car that has about the vary same properties, but with a longer wheelbase. I'd put a little more tire under it because it would be a bit sloppy (transient response) with that high of a rear cornering compliance (just like the car I'm thinking of). You would need to fix the front, too, because if you lower the rear term, the understeer with climb, the gain will drop, as will the max-lat capability.

How's that for a quick armchair analysis (actually, my current chair is 'armless) ?

 

[HJsimpson]

Pat, I'd started to wonder if my initial post could be misinterpreted on some fronts, and it seems that was the case - sorry. I'll try to be be more careful in the future.

Greg, I genuinely wasn't expecting someone to go through it personally, but I'm not silly enough to turn down your offer. The spreadsheet is attached - thank you.

Cibachrome, some of the terms you've used aren't drummed into me just yet. I'll need to do some further reading, before I attempt to pass sensible comment. To be very honest; you're running rings around me. I'm still new to this, and part of this project is for me to use it as a learning exercise. For your reference, this is a kart, and the wheelbase is near the maximum allowed by the class regulations.

I need to do some more reading now...

 

[HJsimpson]

I've been doing some more reading, and I believe the source of the error is that the side-slip angle calculation should have an additional term to account for speed. The side slip angle (beta) in my original calculation is only true for low speeds. I think I understand Cibachrome's second post now too! I've run out of time right now, but I think I'm on the right track...

 

[GregLocock]

I put some rather more digestible numbers in and came up with a few puzzles.

beta and hence alpha vary with wheelbase.

The force generated at the tires (Cs*SA) doesn't seem enough to accelerate the mass at the latacc you want.





Cheers

Greg Locock


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[HJsimpson]

Greg,

My sincere thanks. I'm struggling for time today, but I'll get back to you in a day or two (when I can).

Thanks again.

 

[HJsimpson]

To quote my namesake: Woohoo!

The Beta value simply needed a second term to account for speed. The values now correlate quite well with Cibachrome's, and the tyre forces are now the same magnitude as the applied lateral force.

That's a good start. Going forwards, I'll need to consider load transfer and the applied yaw moment from the rear axle (no differential as it's a kart). That's going to add some complications, but at least I have some foundations to work from now.

Thanks yet again...