1. CoG and Speeding Building SPEED July 28, 2011

2. 28-July-2011 Center of Gravity The Center of Gravity is the point where the object/figure balances Geometry – center of mass of a triangle is the centroid Building SPEED2

3. 28-July-2011 Center of Gravity Point at which all weight of object appears to be concentrated. If object rotates when thrown, the CoG is the center of rotation. Building SPEED3

4. 28-July-2011 Other uses Golf Gymnastics Karate, Running, Swimming Robotics (ASIMO) Building SPEED4

5. 28-July-2011 Other uses Vehicle Rollover Building SPEED5

6. 28-July-2011 Computing From your previous exercise you know that Building SPEED6

7. 28-July-2011 Balance Building SPEED7

8. 28-July-2011Building SPEED8 Front roll center Roll axis Roll moment arm Rear roll center CoG height

9. 28-July-2011 Center of Gravity NASCAR mandate: minimum weight of 1700 lbs on right side. (3450 lbs total minimum car weight) Keep as much weight as possible on left side, so assume put 1750 lbs plus 150-lb driver on left 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 SPEED9

10. 28-July-2011 1986 Race Car Building SPEED10

11. 28-July-2011 StockCarScience Blog Building SPEED11 2007 Chevy Impala Car of Tomorrow

12. 28-July-2011 StockCarScience Blog 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. Building SPEED12

13. 28-July-2011 StockCarScience Blog Braking causes a transfer of some weight from rear to front More weight on front tires than on the rear tires when 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 SPEED13

14. 28-July-2011 StockCarScience Blog Car’s grip is proportional to how hard the wheels are being pushed into the track. Braking: 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 height off the ground of the center of gravity Building SPEED14

15. 28-July-2011 StockCarScience Blog CoG height of 15”, on a left turn, weight transfer leaves you with about 920 lbs of force on the left-side tires and 2680 lbs on the right-side tires Left Turns ONLY CoG height of 17.5” and all else the same, there are 770 lbs on left tires and 2830 lbs on right tires. Lost 150 lbs of grip on left side with higher CoG. You can only go as fast as tire with least amount of grip, so more weight transfer means less grip. Building SPEED15

16. 28-July-2011 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 SPEED16

17. 28-July-2011 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 SPEED17

18. 28-July-2011 CoG Height For a Sprint Cup car CoG is about 17.67 inches above the ground. Compare that to the center of gravity height of an SUV, which is in the 30 inch range. Building SPEED18

19. Pit Road Speeds How does the driver keep from speeding on pit road without a speedometer? 28-July-2011Building SPEED19

20. The Power Path 28-July-2011Building SPEED20 Crankshaft TransmissionDriveshaft Rear end gear Rear Axle Rear wheels

21. Transmission First - the transmission There are 5 sets of gears in a NASCAR race car 4 forward gears, plus reverse. First through third gears decrease the rotation rate coming from the engine; 4 th gear leaves rotation rate unchanged 28-July-2011Building SPEED21

22. Rear-end gear NASCAR gives the teams two or three choices for rear ‐ end gears at each track. At Watkins Glen, for example is a 4.22:1 gear ratio. The input to the rear ‐ end gear makes 4.22 rotations for every 1 rotation the larger gear makes. 28-July-2011Building SPEED22

23. Spur gears Drive gear Follow gear 20:7  2.86:1 gear ratio 28-July-2011Building SPEED23

24. Spur gears 20:10  2.00:1 gear ratio 28-July-2011Building SPEED24 20:5  4.00:1 gear ratio 20:15  1.33:1 gear ratio

25. 28-July-2011Building SPEED25 10 teeth 20 teeth15 teeth

26. Basic Equation n d = number of teeth, drive gear n f = number of teeth, follow gear ω d = rotational speed, drive gear ω f = rotational speed, follow gear 28-July-2011Building SPEED26

27. Example n d = 20, n f = 15, ω d = 60 rpm ω f = ? 28-July-2011Building SPEED27

28. Random Car 28-July-2011Building SPEED28

29. 2011 Dodge Charger ST Gear Ratios:Rear End 1 st gear:2.97:1 3.92:1 2 nd gear:2.10:1 3 rd gear:1.46:1 4 th gear:1.00:1 5 th gear:0.74:1 6 th gear:0.50:1 28-July-2011Building SPEED29

30. 2011 Dodge Charger ST If tachometer reads 3500 rpm in 1 st gear, how fast is the driveshaft rotating? 28-July-2011Building SPEED30

31. 2011 Dodge Charger ST 3500 rpm how fast is the driveshaft rotating in each gear? 28-July-2011Building SPEED31 Gear1 st 2 nd 3 rd 4 th 5 th 6 th Rotation117816672397350047297000

32. 2011 Dodge Charger ST The next question is how fast are the rear wheels rotating if tachometer reads 3500 rpm? Same problem but use the rear-end gear ratio: 3.92:1 28-July-2011Building SPEED32

33. 2011 Dodge Charger ST In 1 st gear 28-July-2011Building SPEED33

34. 2011 Dodge Charger ST 3500 rpm how fast are the rear wheels rotating in each gear? 28-July-2011Building SPEED34 Gear1 st 2 nd 3 rd 4 th 5 th 6 th Rotation300.5425.25611.589312061786

35. 2011 Dodge Charger ST How does this translate into how fast the car is going? In 1 st gear, the tire is rotating at 300.5 rpm. Each revolution it travels its circumference, so in one minute it would travel 300.5 x 2 π r 28-July-2011Building SPEED35

36. 2011 Dodge Charger ST This car uses 20” wheels, so r = 20”. We need mph!! 28-July-2011Building SPEED36

37. 2011 Dodge Charger ST 3500 rpm how fast is the car moving in each gear? 28-July-2011Building SPEED37 Gear1 st 2 nd 3 rd 4 th 5 th 6 th Rotation300.5425.25611.589312061786 Speed(mph)35.7650.6072.76106.26143.5212.53