Avarage Cg of an FSAE Vehicle

[Aditya RS]

I was searching around, but I couldn't find the average cg height that seasoned FSAE teams achieve with their vehicle.

Can some one fill me in?
Thanks in advance.

[Aditya RS]

I was searching around, but I couldn't find the average cg height that seasoned FSAE teams achieve with their vehicle.

Can some one fill me in?
Thanks in advance.

[Bemo]

Why does the cg height of other teams even bother you? Try to get the cg of your car as low as possible and that's it.

[Aditya RS]

I was hoping to get a number. But anyways thanks.

[Tickers]

It might be interesting to them so they can compare. Everyone likes to know how they compare to everyone else, even on trivial things.

That said, I have no idea what our CG height is.

[bminus]

~10 in. above ground.

[Pennyman]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by bminus:
~10 in. above ground. </div></BLOCKQUOTE>

Or 11 with a driver, and no dry sump.

It's fairly simple trig to calculate how low the CG has to be to pass the tilt test, so every car is going to have a CG below that threshold.

[Goost]

Ten to eleven is about right for us. Pennyman has a good point. The tilt test is a good way to find a max value, but you seem to want some comparison for a 'good' CG. Our 2011 car's CG is about 10.76, and we have a wet sump.

[Aditya RS]

Great help.Thanks for the input. http://fsae.com/groupee_common/emoticons/icon_smile.gif

But, your resultant forces act bout the cg, so dont u think its important to know the exact position of it?

am i thinking in the right direction?

[Adambomb]

That is correct. And 10-11" sounds about average for a good car.

[Goost]

Yes, it is very important, and yes forces act at the CG (about the roll and pitch axes). The thing about it is FSAE teams aren't NASA; our CG spreadsheets aren't correct within .04% of the calculated CG like theirs are. Until you have the actual car, and know you will not make a single other change to it before competition, one can only be so accurate when measuring CG height. For example changes to wings, paint and powder coat, different drivers etc. affect the CG (though slightly). So really 1/10" is about as accurate as can be maintained consistently. If you do some basic weight transfer calculations and compare with tire data you can see the significance of that small a change in CG height. I just ran a simulation:
a 10.65" CG vs a 10.75" CG corresponds to 0.0192 faster skid-pad time, less than a 0.5% change in lap time (increase of 0.84 pounds lateral force). A driver practicing for fifteen minutes can make a larger change than that!
I guess that's kinda the whole goal of building a new car every year: you have to determine what battles are worth fighting and how perfect you can actually be in the time given.

[manifold]

don't worry about your cg height mate, just keep it less than 11 in for a good set up .
cheers

[mech5496]

Sorry for the "back from the dead" post but I'm quite puzzled here. We measured our actual CG height today using various methods, with and without drivers, but the measured values really got me thinking... We attached an inclinometer to the chassis, and tilted the car with a hoist. Once it gets close to the balance point, we let just one person move it until it feels balanced, then record the tilt angle and calculate CG height via triangles. The thing is we get values around 90mm, which seems lower than I was -even in my dreams- hoping. Any thoughts on that?!

[Adambomb]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by mech5496:
Sorry for the "back from the dead" post but I'm quite puzzled here. We measured our actual CG height today using various methods, with and without drivers, but the measured values really got me thinking... We attached an inclinometer to the chassis, and tilted the car with a hoist. Once it gets close to the balance point, we let just one person move it until it feels balanced, then record the tilt angle and calculate CG height via triangles. The thing is we get values around 90mm, which seems lower than I was -even in my dreams- hoping. Any thoughts on that?! </div></BLOCKQUOTE>

Yeah, that seems unrealistically low. Just looked up the measurements for ours, granted all I kind find from home at the moment are our '09 specs, but they are from a relatively CG height minimized car. It was 274 mm, with driver. I think for 90 mm you would need a lot of ballast on the bottom of the car, or have the driver laying on his back http://fsae.com/groupee_common/emoticons/icon_smile.gif

One critical factor is the fact that your ground-car interface is squishy tires. Especially once you start rolling the car to the point it's mostly on its sidewalls. For ours we made some big, square, sort of cup things to seat the tires in before CG height testing. Sort of shaped like a big piece of angle iron. They give you a nice, hard, square fulcrum to pivot on. Also if I remember right we did it with the suspension blocked at mid-travel.

It is sort of a hot topic, I've heard from other sources that the only way to do it right is to roll it backward (like it's doing a monster wheelie). That sort of makes sense too as the tire is still sitting on its round side. Unfortunately we've never tested our method back to back with this one for comparison.

[Mike Cook]

First off, your doing some calculations wrong. There will be error with this method, but not that much. Most CG's for fsae cars are in the range of about 10-12 inch.

I've done CG's a lot of different ways, and for race cars the best way to do it is to hang is straight up and down. Then get one of those laser levelers that project in a plane and move it until it intersects with the center of the pivot you are lifting the car by. Let it project on the side of the car and tape some cardboard on the side of the car. Trace the laser line onto the cardboard. Put the car down on scales next and draw a vertical line on the side (you know this location by your percent rear weight). The intersection of the two lines is your cg.

Of course some things:
Probably don't want to do this with fluids in the car that can leak out.
You should lock the suspension from moving.
Be careful.

[Z]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by mech5496:
... we get values around 90mm, which seems lower than I was -even in my dreams- hoping. Any thoughts on that?! </div></BLOCKQUOTE>
Harry,

As Adambomb says, you are probably measuring your CG height above a plane near the top of your sidewalls.

I would suggest a method similar, but different, to Mike's. This way you get most of your important mass distribution numbers. (Note; any rigid body needs ten numbers for a complete "mass" description; 1 from the zeroth MoI = total mass, 3 from first MoI = CG position, 6 from second MoI = 3x principal axes + 3x radii of gyration (or 2nd MoIs).)

You need a strongish overhead beam that you can hang your car from. Or else borrow your little sister's swing set. Or make something like the frame for a playground swing. Or use a stout tree branch (it works, but difficult on a windy day).

Now with car coords X = longitudinal, Y = lateral, Z = vertical, tilt the car like you said, but all the way so Y is now vertical (wrt ground). Use ropes, chains, whatever, to hoist the car so it is hanging freely. It helps to fabricate an angle-iron frame that you fix rigidly to the side of the car, and do the hoisting off this frame.

With the car hanging from a single point (eg. top chain link on overhead beam) you find the CG directly underneath this point. This is easier if you can adjust the chains, say with turnbuckles and different holes in the hoisting frame, so that car X & Z is horizontal, and Y is vertical. Use a carpenter's bubble-level for this, and/or plumb-bobs. EG. a plumb is attached 300mm offset from the car suspension point on overhead-beam, you measure 100mm horizontally from the plumb wire to the car floor, so CG is 200mm above car floor. This will give you X and Z CG positions (Y on centreline, or from scales).

Next, you arrange for the car to swing freely in the plane of its floor (X,Y). The axis for this swinging (parallel to car Z) is best placed as close to the car's side (and CG) as possible, and done as two suspension points ("knife edges" are good). Now time how long for ten complete (small) swings, and use "compound pendulum" theory (easy) to calculate Yaw radius of gyration, kz.

Now you have the five most important numbers;
1. Total mass
2,3,4. Position X,Y,Z of CG
5. Yaw RoG (kz, or yaw MoI).

This would be much easier to explain with a simple drawing facility, but I hope you get it.

Oh, and take note of Mike's warnings...

Z

[Sormaz]

droooooooop

[Mike Cook]

Good suggestion Z. I actually have a huge rig at work that is designed for swinging tanks to measure inertia. I will see if I can post a document we wrote up on the process.

To measure yaw, what we generally do is take four wires and wrap them around our wheels and hang the car from an overhead beam. With the car hanging you want to twist the car back and forth so it is just pivoting around the z axis. You don't want it to swing back and forth, just twist. Measure the period of twist and you can calculate the inertia of the vehicle from that.

But then I build another rig that is essentially the same except the that we have a swinging platform that you can put the car on. This is better and worse. The platform can potentially add a lot of inertia and really hurt your accuracy. However, for roll and pitch it makes the testing much easier.

For roll and pitch you want the whole vehicle to swing about the x or y axis. For our swing table we have struts that come up to a pillow block and go down to our platform.

Anyways,
Remember you want the pivots close to the CG....

[mech5496]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by Adambomb:
One critical factor is the fact that your ground-car interface is squishy tires. Especially once you start rolling the car to the point it's mostly on its sidewalls. For ours we made some big, square, sort of cup things to seat the tires in before CG height testing. Sort of shaped like a big piece of angle iron. They give you a nice, hard, square fulcrum to pivot on. Also if I remember right we did it with the suspension blocked at mid-travel.

It is sort of a hot topic, I've heard from other sources that the only way to do it right is to roll it backward (like it's doing a monster wheelie). That sort of makes sense too as the tire is still sitting on its round side. Unfortunately we've never tested our method back to back with this one for comparison. </div></BLOCKQUOTE>

Tried tilt backwards, but unfortunately our hoist doesn't has too much height available so it's virtually impossible to tilt it till the balance point. I think that the main problem is the pivot point. I will try to replace the "pivoting" side wheels with some rigid steel replacements I have made and measure it again...
Z your method sounds really interesting, but not applicable right now, as we have to spend a full day to build the rig. It might worth it though....http://fsae.com/groupee_common/emoticons/icon_biggrin.gif

[mech5496]

OK, did it again, and it was impossible to think that tires did actually contribute to that error... This time we changed the "pivoting" right side wheels with steel replacements and rolled the car until balance point. Then we did the same by tilting the nose up, and we got about the same value (2-3mm difference actually). Now we have a number that makes absolute sense (226mm)... We have also recorded weight values on the pivoting wheels at various tilt and roll angles, so we will be able to calculate the CG height by those too. Now I want really badly to measure inertias....http://fsae.com/groupee_common/emoticons/icon_smile.gif

[Z]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by mech5496:
Now I want really badly to measure inertias....http://fsae.com/groupee_common/emoticons/icon_smile.gif </div></BLOCKQUOTE>
Harry,

You might be able to do a quick and cheap yaw inertia test as follows. Tilt car onto its side. Strap a stout wooden beam (say 100x100mm x 2m long) to the side of the car near its CG (use "tie-down" straps that look like heavy duty seat belts, and cardboard packing). The beam should now be horizontal and parallel to car Z. Support the ends of the beam on heavy duty work benches so the car is completely off the ground. Put some angle iron pieces between the beam and work benches (as "V") to act as "knife-edge" pivots.

The car should now be able to swing freely in the plane of its floor. Time ten small swings, divide by ten to get the period T. Check the following, but I think the formulae are;

a = distance of CG below pivot axis (you must measure this based on known CG position),
a+b = g.(T/(2.pi))^2 = equivalent length of a simple pendulum (you measure T, guess g (9.81?), and derive b),
k^2 = ab,
with k = yaw radius of gyration.

Z

[Chris Texas]

Here's a power point that I used when I did inertia on UT's car last year. It also has a picture of the jig with the car. I believe you can do all axis with it too. If you have the use for all three.

http://www.me.utexas.edu/~dscl...d_Pendulum_Model.pdf (http://www.me.utexas.edu/%7Edsclab/leks/3_Compound_Pendulum_Model.pdf)

Chris Drew
Applied Mechanics Engineer, Cummins Diesel 2011-present
Junior Engineer, Racers Edge Motorsports 2011
Team Captain, UT FSAE 2009-2011
Suspension and Lead Engineer UT FSAE 2009-2011
Machinist, Welder, Fabricator 2006-2011

[mech5496]

Chris,

Thanks for the .pdf as it is really analytical about what you did. That was exactly what I had in mind when I said "complicated"... :P

Z, I'm not quite sure I understood your suggestion. With X axis-&gt;longitudinal, Z axis-&gt; vertical and pointing the sky, what I thought I have to do is let it rotate (swing) around Z axis or an axis parallel to Z, with the (0,0,0)point being the CG. Am I getting something wrong here?

[Z]

Harry,

There are two different types of "pendulum" being discussed here.

1. Torsional Pendulum - rotation about vertical axis.
================================================== ==
This type is shown on pages 18 & 19 of Chris's pdf.

For: More precise. Car stays normal way up, so drive-on, drive-off, which is why this type is common in the auto industry.

Against: Requires at least three suspension points high up that carry the platform + car weight (eg. "trifilar" pic on p19 above). So a substantial "framework" must be built, or bolt to strong roof beams. All wires should be initially vertical, equal length, and equidistant from the car CG.

2. Compound Pendulum - rotation about horizontal axis.
================================================== ====
This type is shown on page 10 of Chris's pdf, and is what I was suggesting. (A "simple pendulum" is like pic on p10, but with a "point mass" on the end of a "massless rod", so no MoIs.)

For: Maybe quicker and easier. Only two suspension points required, and lower down, so less framework. Can use same frame to find car's CG height.

Against: A bit less precise (but depends on lots of things). Car must be tilted onto side (ie. car Z axis must now be horizontal), so fluids pour out, suspension extends (should be locked at ride height), difficult to do with big trucks, etc.
~~~~~o0o~~~~~

Chris's analysis included damping so is more complicated than necessary. Both types can be understood with simple maths.

Z

[Z]

Here is a sketch...

https://lh6.googleusercontent.com/-GcdYo4Vsw4Y/Tuacd9zMn6I/AAAAAAAAAG8/FHSECGHh_Cs/s400/YawInertiaRig.jpg

Z

[mech5496]

<BLOCKQUOTE class="ip-ubbcode-quote"><div class="ip-ubbcode-quote-title">quote:</div><div class="ip-ubbcode-quote-content">Originally posted by mech5496:
...what I thought I have to do is let it rotate (swing) around Z axis or an axis parallel to Z... </div></BLOCKQUOTE>

That's exactly what I had in mind! Thanks!