Center of Gravity

1. Center of Gravity Building SPEEDNovember 20, 2010

2. 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 SPEED

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

4. Other uses Golf Gymnastics Karate, Running, Swimming Robotics (ASIMO) Building SPEED

5. Other uses Vehicle Rollover Building SPEED

6. Computing From your previous exercise you know that Building SPEED

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

8. Balance Building SPEED

9. CoG height Front roll center Rear roll center Roll axis Roll moment arm Building SPEED

10. 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 SPEED

11. 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 SPEED

12. 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 SPEED

13. 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 SPEED

14. Roll Moment Arm All NASCAR cars have a wheelbase of 110 inches. Find A and B. Building SPEED

15. 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 SPEED

16. 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 SPEED

17. 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. Building SPEED

18. StockCarScience Blog Josh Browne says that the height of the CoGin 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 SPEED

19. 1986 Race Car Building SPEED

20. 2001 Earnhardt Intimidator Building SPEED

21. StockCarScience Blog 2002 Ford Taurus Building SPEED

22. StockCarScience Blog 2007 Chevy ImpalaCar of Tomorrow Building SPEED

23. StockCarScience Blog 2007 Chevy ImpalaCar of Tomorrow Building SPEED

24. StockCarScience Blog Josh Browne says that the height of the CoGin 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 SPEED

25. 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 SPEED

26. StockCarScience Blog Car’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 Building SPEED

27. StockCarScience Blog Acceleration is in g’s. Building SPEED

28. StockCarScience Blog Building SPEED

29. StockCarScience Blog Appeal to symmetry, that is assume a 3600 lb race car with the weight equally distributed on each side 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”. 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 SPEED

30. StockCarScience Blog Raise 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 SPEED

31. 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 SPEED

32. 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 car’s side force? Building SPEED

33. 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 SPEED

34. 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 SPEED

35. Determining CoG Height Find the angle at which rear end raised. E is the opposite side and the wheelbase, WB, is the hypotenuse Building SPEED

36. 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 SPEED

37. 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 SPEED

38. Determining CoG Height WB = 110 D = 1225 — 1200 W = 2500 α = 12.6˚ Building SPEED

39. Determining CoG Height • CGH = 4.92 inches • Ground to center line of the wheels = 12.75 inches • CoGis 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 SPEED

40. 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 SPEED