... anyone got an value of inertia of a formula student car in roll, pitch and yaw ??? thanks !

Yes.

quote:

Originally posted by Denny Trimble:
Yes.

can you please tell me the values (just roughly)you've got from your FSAE car ? thanks !

Well, I don't mean to be rude, but we've spent considerable effort and time building test equipment and measuring the inertia of our cars, as well as modeling as many parts as possible in CAD, to get a good estimate early in the design stage.

I don't think our hard-working team-members would appreciate me sharing that info.

If you're working on a simulation that needs inertia inputs, I recommend you make educated guesses, then check them with physical testing later.

2, 4 and 6

what you really want to ask is ..

"what are typical radii of gyration for these cars?"

in the absense of measuring I'd guess

300 mm roll
600 mm yaw
600 mm pitch

Frank

After making some random MMOI rigs doing everything wrong (too heavy, too much friction, random things wrong with them, dodgy measurements, random joker making them....) they worked measuring MMOI of moderate (150kg) steel objects of known geometry. When it came to putting a 220-300kg vehicle on them it would give very reasonable values in certain axis, (i think yaw in particular). When i get back to civilisation again ill look up some old notes and confirm it. Otherwise it was all just luck. (unless someone in brisvegas can look through my "Epic Tome" of a thesis and confirm it)

*End of random mutterings now*

Back-of-envelope calcs...

Assume car+driver = 300kg, wheelbase = 1.5m, track = 1.2m, weight distribution = 50:50.

Now assume (!!!) car+driver is homogenous rectangular solid L=1.5m, W=1.0m, H=0.5m. So Izz = M(LxL+WxW)/12, Kzz = sqrt((LxL+WxW)/12), etc.


Yaw:
Iyaw = 300(1.5x1.5+1.0x1.0)/12 = 81.25kg.m.m
Kyaw = sqrt((1.5x1.5+1.0x1.0)/12) = 0.52m
k.k/ab = (0.52x0.52)/(0.75x0.75) = 0.48

Pitch:
Ip = 62.5kg.m.m
Kp = 0.46m
k.k/ab = 0.37

Roll:
Ir = 31.25kg.m.m
Kr = 0.32m
k.k/ab = 0.29


For dynamic analysis pitch and roll inertias should be calculated without wheels, so above Ip & Ir are overestimates.

So, Denny, how does that compare with the CAD work?

Z

(Edit note: Manshing, The above estimate of rectangular car size is to the nearest half metre. If you use a tape measure on the major components, and MoI and parallel axes equations, etc., then you should get better results.)

This message has been edited. Last edited by: Z,

quote:

Originally posted by Z:

So, Denny, how does that compare with the CAD work?

Z

Pretty close on roll, but about 40% low on pitch and yaw, for the entire vehicle with driver. Our car has a longer wheelbase, though. Also, our unsprung weight is significant (and we work hard to reduce it), and at the corners of the "rectangle". The (mass * distance^2) term adds up quickly at the corners.

Denny,

Sooo,.. have you also got your Products of Inertia, and/or the angles to your Principle Axes?

I'm pretty sure the judges want to know that...

Z

Yes, SolidWorks gives all of that information by default.

Just kidding about the judges...

Out of curiosity, what is the angle (roughly) between the car (floor plane) and principle X axes?

Z

quote:

Originally posted by Z:
Just kidding about the judges...

Out of curiosity, what is the angle (roughly) between the car (floor plane) and principle X axes?

Z

Yeah, I figured as much... it's still hard for me to judge an Aussie's sense of humor sometimes

Here are our principle axes expressed in the vehicle coordinate system (x rearward, y right, z up):

Ix = (0.99998007, 0.00332047, 0.00537001)

Iy = (-0.00331226, 0.99999333, -0.00153766)

Iz = (-0.00537508, 0.00151984, 0.99998440)

This is for the full vehicle with driver and unsprung mass. The sprung mass principal Iy and Iz axes are very slightly rotated about (.997ish) about x, but Ix is still .9999.

I'd convert these to angles, but it's a little late/early, and I need to start getting ready for a 3 hour time zone swap, the hard way

Thanks for that.

5mm/m on the longitudinal up/down axis is what I expected (ie. pretty low). A bit surprising is the 3mm/m left/right deviation of this axis - I guess an offset radiator? (Or mutant driver - bigger right foot?? )

Z

So what exactly do these numbers tell you car wise? Is it good, bad, what do you compare it too etc. Our team has some values too but for me it's hard to grasp what we can do with these numbers as in where do we stand with our numbers and what are considered good numbers. Yeah we can go of the numbers we have now but what is the purpose when we don't fully grasp what they mean. Do any of you guys care to enlighten me on what the heck these roll,yaw, pitch numbers mean??

My apologies, I was talking abou the moments of inertias above.

For "mass distribution" of FSAE cars there are only two numbers that are really important - CG height and Yaw inertia. Both should be as low as possible. CG should be low for low "weight transfer" during acc/brk/cornering (and hence less chance of rollover, etc.). Yaw inertia should be low for low resistance to change in direction, hence a more agile/nimble car.

Alternatively, you can think in terms of CGheight/Track, and Yaw radius of gyration relative to wheelbase (Kyaw/WB). CGheight/Track should be less than about 0.5 (Edit note: Oops! I was thinking in terms of Track/2. Actually, CG/Track should be less than 0.25) - think about the tilt test! Kyaw/WB should be well under 0.5 for agile handling. About the best you can do (because of the mass of the wheels) is about Kyaw/WB=0.25.

So compare these numbers to the opposition, and your previous cars, and try to go lower next year.

Z

PS. Kyaw/WB is more commonly expressed as K^2/ab ("K-squared-a-b") where a=distance front axle to CG, b=distance rear axle to CG. So, roughly, Kyaw/WB = ~ 1/2 x sqrt(K^2/ab).

This message has been edited. Last edited by: Z,

quote:

Originally posted by Z:
For "CG should be low for low "weight transfer" during acc/brk/cornering (

hmmmmm CG low for accelaration???? only if you have an all wheel drive car.

Ash

Ashley,

I note that most FSAE cars have an approximate 50:50 F:R weight distribution, and most can spin their rear wheels when exiting slow corners.

I see three possible cures for the wheel spin: 1) less power; 2) higher CG; 3) more rear weight percentage. Of these I would definitely go for the third (say, about 40:60), with bigger rear tyres to maintain cornering balance. I would then keep trying to lower the CG. (I think the disadvantages of options 1 & 2 are obvious...)

This approach is a bit old-fashioned (like me ) but I reckon it is 90% of the reason for putting the engine in the back. Seems to work ok on 2WD drag cars...

Z

Hi Eric,

i totally agree mate....just thought ide straighten out what u said earlier about low CoG being an advantage in accelaration when it isnt....i knew u knew it wasnt but i couldnt resist posting! haha

in our case 46:54 is the target, we are a little rear heavy at the moment (43:57ish with the engine next to the driver. Low CoG is a constant aim for sure....i think we would have been about the lowest at SAE-A last year we also probably had the lowest MOI in yaw.


cheers

Ash