CoG and Speeding
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CoG and Speeding Building SPEED July 28, 2011
description
CoG and Speeding. Building SPEED July 28, 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. Center of Gravity. Point at which all weight of object appears to be concentrated . - PowerPoint PPT Presentation
Transcript of CoG and Speeding
CoG and SpeedingBuilding SPEEDJuly 28, 2011
Building SPEED 228-July-2011
Center of GravityThe Center of Gravity is the point where the object/figure balances
Geometry – center of mass of a triangle is the centroid
Building SPEED 328-July-2011
Center of GravityPoint at which all weight of object appears to be concentrated. If object rotates when thrown, the CoG is the center of rotation.
Building SPEED 428-July-2011
Other usesGolf
Gymnastics
Karate, Running, Swimming
Robotics (ASIMO)
Building SPEED 528-July-2011
Other usesVehicle Rollover
Building SPEED 628-July-2011
ComputingFrom your previous exercise you know that
1 1 2 2 1
1 2
1
k
i ik k i
kk
ii
m rm r m r m rCoGm m m m
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Balance
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Front roll centerRoll axis
Roll moment arm
Rear roll center
CoG height
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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.
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1986 Race Car
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StockCarScience Blog2007 Chevy Impala
Car of Tomorrow
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StockCarScience 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.
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StockCarScience BlogBraking 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 SPEED 1428-July-2011
StockCarScience BlogCar’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 SPEED 1528-July-2011
StockCarScience BlogCoG 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 SPEED 1628-July-2011
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)
Building SPEED 1728-July-2011
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?
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CoG HeightFor 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.
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Pit Road SpeedsHow does the driver keep from
speeding on pit road without a speedometer?
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The Power Path
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Crankshaft Transmission Driveshaft
Rear end gear
Rear Axle
Rear wheels
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TransmissionFirst - the transmissionThere 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;4th gear leaves rotation rate unchanged
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Rear-end gearNASCAR 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.
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Spur gearsDrive gearFollow gear20:7 2.86:1 gear
ratio
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Spur gears
20:10 2.00:1 gear ratio
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20:5 4.00:1 gear ratio
20:15 1.33:1 gear ratio
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10 teeth 20 teeth 15 teeth
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Basic Equationnd = number of teeth, drive gearnf = number of teeth, follow gearωd = rotational speed, drive gearωf = rotational speed, follow gear
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· ·d d ffn n
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Examplend = 20, nf = 15, ωd = 60 rpmωf = ?
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·
2060 40 rpm15
df d
f
nn
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Random Car
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2011 Dodge Charger STGear Ratios: Rear End1st gear: 2.97:1 3.92:12nd gear: 2.10:13rd gear: 1.46:14th gear: 1.00:15th gear: 0.74:16th gear: 0.50:128-July-2011
Building SPEED 30
2011 Dodge Charger STIf tachometer reads 3500 rpm in
1st gear, how fast is the driveshaft rotating?
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·
13500 1178 rpm2.97
df d
f
nn
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2011 Dodge Charger ST3500 rpm how fast is the
driveshaft rotating in each gear?
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Gear 1st 2nd 3rd 4th 5th 6th
Rotation 1178 1667 2397 3500 4729 7000
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2011 Dodge Charger STThe 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
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2011 Dodge Charger STIn 1st gear
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11178 300.5 rpm3.92
df d
f
nn
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2011 Dodge Charger ST3500 rpm how fast are the rear
wheels rotating in each gear?
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Gear 1st 2nd 3rd 4th 5th 6th
Rotation 300.5 425.25 611.5 893 1206 1786
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2011 Dodge Charger STHow does this translate into how
fast the car is going?
In 1st 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 2πr
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Building SPEED 36
2011 Dodge Charger STThis car uses 20” wheels, so r = 20”.
We need mph!!
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·2 300.5(2)( )(20) 12020in37762
min
v r
in 1 ft 1 m 60 min37762min 12 in 5280 ft 1 hr
35.76 mph
v
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2011 Dodge Charger ST3500 rpm how fast is the car
moving in each gear?
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Gear 1st 2nd 3rd 4th 5th 6th
Rotation 300.5 425.25 611.5 893 1206 1786
Speed(mph) 35.76 50.60 72.76 106.26 143.5 212.53
