November 20 2010 20Nov2010 Center of Gravity Early introduction is Center of Gravity is the point where the objectfigure balances Geometry center of mass of a triangle is For a polygonal figure the center of mass is the barycenter under some definitions ID: 1019210
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1. Center of GravityBuilding SPEEDNovember 20, 2010
2. 20-Nov-2010Center of GravityEarly introduction is Center of Gravity is the point where the object/figure balancesGeometry – center of mass of a triangle isFor a polygonal figure the center of mass is the barycenter (under some definitions)Building SPEED2
3. 20-Nov-2010Center 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.Building SPEED3
4. 20-Nov-2010Other usesGolfGymnasticsKarate, Running, SwimmingRobotics (ASIMO)Building SPEED4
5. 20-Nov-2010Other usesVehicle RolloverBuilding SPEED5
6. 20-Nov-2010ComputingFrom your previous exercise you know that Building SPEED6
7. 20-Nov-2010Known 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.Building SPEED7
8. 20-Nov-2010BalanceBuilding SPEED8
9. 20-Nov-2010Building SPEED9Front roll centerRoll axisRoll moment armRear roll centerCoG height
10. 20-Nov-2010Roll 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?Building SPEED10
11. 20-Nov-2010Roll Moment ArmCornering 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.Building SPEED11
12. 20-Nov-2010Roll Moment ArmRoll Moment Arm = MACGH = center of gravity heightWB = wheelbase (distance between front and rear axles)RCF = front roll center heightRCR = rear roll center height Building SPEED12
13. 20-Nov-2010Roll Moment ArmWeight 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 %Building SPEED13
14. 20-Nov-2010Roll Moment ArmAll NASCAR cars have a wheelbase of 110 inches. Find A and B.Building SPEED14
15. 20-Nov-2010Roll Moment ArmIf 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.Building SPEED15
16. 20-Nov-2010Roll Moment ArmFind 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.Building SPEED16
17. 20-Nov-2010StockCarScience BlogNASCAR 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.Building SPEED17
18. 20-Nov-2010StockCarScience BlogJosh 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.Building SPEED18
19. 20-Nov-20101986 Race CarBuilding SPEED19
20. 20-Nov-20102001 Earnhardt IntimidatorBuilding SPEED20
21. 20-Nov-2010StockCarScience BlogBuilding SPEED212002 Ford Taurus
22. 20-Nov-2010StockCarScience BlogBuilding SPEED222007 Chevy ImpalaCar of Tomorrow
23. 20-Nov-2010StockCarScience BlogBuilding SPEED232007 Chevy ImpalaCar of Tomorrow
24. 20-Nov-2010StockCarScience BlogJosh 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.Building SPEED24
25. 20-Nov-2010StockCarScience BlogBraking creates torque transferring some weight from rear to frontThis 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.Building SPEED25
26. 20-Nov-2010StockCarScience 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 rearAmount of weight that shifts is proportional to how high off the ground the center of gravity is Building SPEED26
27. 20-Nov-2010StockCarScience BlogAcceleration is in g’s. Building SPEED27
28. 20-Nov-2010StockCarScience BlogBuilding SPEED28
29. 20-Nov-2010StockCarScience BlogAppeal to symmetry, that is assume a 3600 lb race car with the weight equally distributed on each sideTrack (or tread width) = distance between the two wheels. In a NASCAR car, the track must be between 61-1/4” to 61-1/2”.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 tiresLeft Turns ONLYBuilding SPEED29
30. 20-Nov-2010StockCarScience BlogRaise the CG to 17.5”. Keeping everything the same acceleration and track, there are 770 lbs on the left-side tires and 2830 lbs on the right-side tires. Lost 150 lbs of grip on the left side just by raising the CG. You can only go as fast as the tire with the least amount of grip, so more weight transfer means less grip.Building SPEED30
31. 20-Nov-2010StockCarScience BlogSome drivers have suggested lowering CoG Would make a big difference in how the cars handleHeight of the CoG determined by mass distributionTo 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)Building SPEED31
32. 20-Nov-2010StockCarScience BlogOr must move mass from the top of the car to the bottom without compromising safetyCould make cars wider to decrease the weight transferWhat would that do to the car’s side force?Building SPEED32
33. 20-Nov-2010Determining 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.Building SPEED33
34. 20-Nov-2010Determining CoG HeightRaise the rear end of car a fixed height, EThe weight of the car will be redistributed and we front tires now carry more weight, say1225 pounds. Building SPEED34
35. 20-Nov-2010Determining CoG HeightFind the angle at which rear end raised. E is the opposite side and the wheelbase, WB, is the hypotenuseBuilding SPEED35
36. 20-Nov-2010Determining 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˚.Building SPEED36
37. 20-Nov-2010Determining CoG HeightD = 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 groundBuilding SPEED37
38. 20-Nov-2010Determining CoG HeightWB = 110D = 1225 — 1200W = 2500α = 12.6˚Building SPEED38
39. 20-Nov-2010Determining CoG HeightCGH = 4.92 inchesGround to center line of the wheels = 12.75 inchesCoG 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. Building SPEED39
40. 20-Nov-2010Determining 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.Building SPEED40