1. Center of Gravity Building SPEED November 20, 2010

2. 20-Nov-2010 Center of Gravity Early 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) Building SPEED2

3. 20-Nov-2010 Center of Gravity Point 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-2010 Other uses Golf Gymnastics Karate, Running, Swimming Robotics (ASIMO) Building SPEED4

5. 20-Nov-2010 Other uses Vehicle Rollover Building SPEED5

6. 20-Nov-2010 Computing From your previous exercise you know that Building SPEED6

7. 20-Nov-2010 Known Locations CoG of 2 particle system lies on line connecting them. CoG closer to more massive object. CoG of a ring - at center of ring CoG of solid triangle at centroid (average of 3 vertices) The CoG of rectangle - at intersection of 2 diagonals. Building SPEED7

8. 20-Nov-2010 Balance Building SPEED8

9. 20-Nov-2010Building SPEED9 Front roll center Roll axis Roll moment arm Rear roll center CoG height

10. 20-Nov-2010 Roll Axis Roll 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-2010 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. Building SPEED11

12. 20-Nov-2010 Roll Moment Arm Roll Moment Arm = MA CGH = center of gravity height WB = wheelbase (distance between front and rear axles) RCF = front roll center height RCR = rear roll center height Building SPEED12

13. 20-Nov-2010 Roll Moment Arm Weight of cars not evenly distributed between front and rear axles More weight in rear => car handles better Optimal percentage 52% in rear, 48% in front In Moment Arm formula A = wheelbase x rear wt % B = wheelbase x front wt % Building SPEED13

14. 20-Nov-2010 Roll Moment Arm All NASCAR cars have a wheelbase of 110 inches. Find A and B. Building SPEED14

15. 20-Nov-2010 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. Building SPEED15

16. 20-Nov-2010 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. Building SPEED16

17. 20-Nov-2010 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 well assume that they put 1750 lbs of the cars weight plus a 150-lb driver on the left-hand side. The center of gravity is a little to the left of the cars centerline and close to the midpoint of the car front/back. Building SPEED17

18. 20-Nov-2010 StockCarScience Blog Josh Browne says that the height of the CoG in the new car is about at the drivers tush. Thats 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-2010 1986 Race Car Building SPEED19

20. 20-Nov-2010 2001 Earnhardt Intimidator Building SPEED20

21. 20-Nov-2010 StockCarScience Blog Building SPEED21 2002 Ford Taurus

22. 20-Nov-2010 StockCarScience Blog Building SPEED22 2007 Chevy Impala Car of Tomorrow

23. 20-Nov-2010 StockCarScience Blog Building SPEED23 2007 Chevy Impala Car of Tomorrow

24. 20-Nov-2010 StockCarScience Blog Josh Browne says that the height of the CoG in the new car is about at the drivers tush. Thats 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-2010 StockCarScience Blog Braking 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. Building SPEED25

26. 20-Nov-2010 StockCarScience Blog Cars grip is proportional to how hard the wheels are being pushed into the track. Braking youre 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 Building SPEED26

27. 20-Nov-2010 StockCarScience Blog Acceleration is in gs. Building SPEED27

28. 20-Nov-2010 StockCarScience Blog Building SPEED28

29. 20-Nov-2010 StockCarScience Blog 1.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 Building SPEED29

30. 20-Nov-2010 StockCarScience Blog 1.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. Building SPEED30

31. 20-Nov-2010 StockCarScience Blog Some 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) Building SPEED31

32. 20-Nov-2010 StockCarScience Blog Or 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 cars side force? Building SPEED32

33. 20-Nov-2010 Determining CoG Height Weigh 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-2010 Determining CoG Height Raise 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. Building SPEED34

35. 20-Nov-2010 Determining CoG Height Find the angle at which rear end raised. E is the opposite side and the wheelbase, WB, is the hypotenuse Building SPEED35

36. 20-Nov-2010 Determining CoG Height For 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-2010 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 Building SPEED37

38. 20-Nov-2010 Determining CoG Height WB = 110 D = 1225 1200 W = 2500 α = 12.6˚ Building SPEED38

39. 20-Nov-2010 Determining CoG Height CGH = 4.92 inches Ground to center line of the wheels = 12.75 inches 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. Building SPEED39

40. 20-Nov-2010 Determining CoG Height Find 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