Center of Gravity Building SPEED November 20, 2010

Center of Gravity

Building SPEEDNovember 20, 2010

Building SPEED 220-Nov-2010

Center of GravityEarly introduction is Center of Gravity is the point where the object/figure balances

Geometry – center of mass of a triangle is

For a polygonal figure the center of mass is the barycenter (under some definitions)


Center of GravityPoint at which all of the weight of an object appears to be concentrated. If object rotates when thrown, the CoG is the center of rotation. When object is suspended so can move freely, CoG is always directly below the point of suspension. An object can be balanced on sharp point placed directly beneath CoG.


Other usesGolf

Gymnastics

Karate, Running, Swimming

Robotics (ASIMO)


Other usesVehicle Rollover


ComputingFrom your previous exercise you know that

1 1 2 2 1

1 2

1

k

i ik k i

kk

ii

mrm r m r m r

CGm m m m


Known LocationsCoG of 2 particle system lies on line connecting them. CoG closer to more massive object.CoG of a ring - at center of ringCoG of solid triangle at centroid (average of 3 vertices)The CoG of rectangle - at intersection of 2 diagonals.


Balance


Front roll centerRoll axis

Roll moment arm

Rear roll center

CoG height


Roll AxisRoll axis is the theoretical line which connects the front roll center to the rear roll center.

The roll centers are the points along the axes where the car pivots left and right and up and down when it corners.

The roll axis is the line about which the car rolls when you turn.

Where are roll centers located?


Roll Moment Arm

Cornering forces affect the car at CoG.

The distance between the roll axis and the center of gravity is called the Roll Moment Arm.

Determines how much weight is transferred in cornering.


Roll Moment Arm

Roll Moment Arm = MACGH = center of gravity heightWB = wheelbase (distance between front and rear axles)RCF = front roll center heightRCR = rear roll center height

F RB RC A RC

MA CGHWB


Roll Moment Arm

Weight of cars not evenly distributed between front and rear axlesMore weight in rear => car handles betterOptimal percentage 52% in rear, 48% in frontIn Moment Arm formula A = wheelbase x rear wt % B = wheelbase x front wt %

F RB RC A RC

MA CGHWB


Roll Moment Arm

All NASCAR cars have a wheelbase of 110 inches.

Find A and B.

F RB RC A RC

MA CGHWB


Roll Moment Arm

If the front roll center height is 2.5 inches, the rear roll center height is 11 inches, and the center of gravity height is 15 inches, find the length of the moment arm for the car.

F RB RC A RC

MA CGHWB


Roll Moment Arm

Find the angle of depression from the line parallel to the ground that intersects the center of the front wheel to the bottom of the moment arm. HINT: the wheelbase is 110 inches and the center of gravity is not in the center since 52% of the weight is in the back of the car and 42% of the weight is in the front of the car.


StockCarScience Blog

NASCAR mandates a minimum weight of 1700 lbs (out of the 3450 lbs total minimum car weight) on the right-hand side. Teams like to keep as much weight as possible on the left-hand side, so we’ll assume that they put 1750 lbs of the car’s weight plus a 150-lb driver on the left-hand side. The center of gravity is a little to the left of the car’s centerline and close to the midpoint of the car front/back.



Josh Browne says that the height of the CoG in the new car is about “at the driver’s tush”.

That’s a couple of inches higher than it used to be in the old car.

Why does that matter?

Load transfer.


1986 Race Car


2001 Earnhardt Intimidator



2002 Ford Taurus


StockCarScience Blog2007 Chevy Impala

Car of Tomorrow


StockCarScience Blog2007 Chevy Impala

Car of Tomorrow



Josh Browne says that the height of the CoG in the new car is about “at the driver’s tush”.

That’s a couple of inches higher than it used to be in the old car.

Why does that matter?

Load transfer.


StockCarScience BlogBraking creates torque transferring some weight from rear to front

This means there is more weight on front tires than on the rear tires when the car is braking

Acceleration causes weight transfer from front to back

Cornering causes weight to shift from the inside wheels to the outside wheels.


StockCarScience BlogCar’s grip is proportional to how hard the wheels are being pushed into the track.

Braking you’re transferring weight from the back wheels to the front => losing grip in rear and gaining grip front

Accelerating => losing grip in front and gaining grip rear

Amount of weight that shifts is proportional to how high off the ground the center of gravity is



Acceleration is in g’s.

weight of car acceleration CG heightWeight transferred

track

acceleration CG heightFractional weight transferred 100

track



acceleration CG heightFractional weight transferred 100

track


StockCarScience Blog1. Appeal to symmetry, that is assume a 3600

lb race car with the weight equally distributed on each side

2. Track (or tread width) = distance between the two wheels. In a NASCAR car, the track must be between 61-1/4” to 61-1/2”.

3. With a CG height of 15”, at a lateral acceleration of 1g, the weight transfer leaves you with about 920 lbs on the left-side tires and 2680 lbs on the right-side tires

Left Turns ONLY


StockCarScience Blog1. Raise the CG to 17.5”. 2. Keeping everything the same acceleration

and track, there are 770 lbs on the left-side tires and 2830 lbs on the right-side tires.

3. Lost 150 lbs of grip on the left side just by raising the CG.

4. You can only go as fast as the tire with the least amount of grip, so more weight transfer means less grip.


StockCarScience BlogSome drivers have suggested lowering CoG

Would make a big difference in how the cars handle

Height of the CoG determined by mass distribution

To lower CoG, must increase the total mass of the car (for example by adding mass to the frame rails, but then the engine has to move a larger mass)


StockCarScience BlogOr must move mass from the top of the car to the bottom without compromising safety

Could make cars wider to decrease the weight transfer

What would that do to the car’s side force?


Determining CoG HeightWeigh the car in a known configuration using four scales – one under each tire.

Assume the car weighs 2500 pounds.Since weight is distributed 48% in front, the front scales should read 1200 pounds when the car is level.


Determining CoG HeightRaise the rear end of car a fixed height, E

The weight of the car will be redistributed and we front tires now carry more weight, say1225 pounds.


Determining CoG HeightFind the angle at which rear end raised.

E is the opposite side and the wheelbase, WB, is the hypotenuse

E

sinWB


Determining CoG HeightFor example, if you raised the car with the wheelbase of 110″ up to a height of 24″

then sin(α) = 24/110 = 0.21818 and α = 12.6˚.


Determining CoG Height

D = angled front weight minus the level front weight

W = total car weight.

Compute height above the ground, add this distance to the height of the center line of the wheels above the ground

cotWB DCGH

W


Determining CoG Height

WB = 110D = 1225 — 1200W = 2500α = 12.6˚

cotWB DCGH

W

cot 110 25 cot1.1 4.4729 4.92

2500WB D

CGHW


Determining CoG HeightCGH = 4.92 inchesGround to center line of the wheels = 12.75 inchesÞ CoG is 17.67 inches above the ground.

Compare that to the center of gravity height of an SUV, which will be in the 30 inch range.


Determining CoG HeightFind the center of gravity height of the following car. The wheelbase is 109 inches, level front weight is 1230 pounds, the angled front weight is 1310 pounds, the amount you elevated the rear is 27 inches, and the total weight is 2500 pounds. Assume that you have 12 ¼ inches from the ground to the centerline of the wheels.

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Center of Gravity Building SPEED November 20, 2010