Project

Longitudinal load transfer and pitch compensation

Total weight lbs 3750 Kg 1702.5 Newtons 16462.61
F/R ratio 55% front 2062.5 Kg 936.375 Newtons 9054.437
Weight Rear 1687.5 Kg 766.125 Newtons 7408.176
Wheelbase Inches 98 mm 2489.2
C.G. Height In. 17 mm 431.8 0.173469
Tire radius In. 11.5 mm 292.1
Throttle Acceleration ft/sec^2 16.25 m/s^2 4.87988 0.504658 half a \'g\' accleration
g ft/sec^2 32.2 m/s^2 9.66967
Drive ratio %front 0 %Rear 100
Front spring rate lb/in 450 kg/mm 8.043307 N/mm 77.77612
Rear spring rate lb/in 650 kg/mm 11.61811 N/mm 112.3433
Front spring Motion ratio in/in 0.76 mm/mm 0.76
Rear spring motion ratio in/in 0.72 mm/mm 0.72
Tire rate 1
Front wheel rate (actual) lb/in 259.92 kg/mm 4.645814 N/mm 44.92349
Rear wheel rate (actual) lb/in 336.96 kg/mm 6.022828 N/mm 58.23876
F SVIC vertical distance from contact patch in 13.22 mm 335.788
F SVIC horizontal distance from contact patch in 28.5 mm 723.9
R SVIC vertical distance from contact patch in 16 mm 406.4
R SVIC horizontal distance from contact patch in 42.5 mm 1079.5

Load Transfer due to motion:

Static loading due to weight distribution: N kg (N/g) lbs/g
Wfront 9054.43694 2062.5
Wrear 7408.17568 1687.5
Dynamic Loading due to acceleration [dW] 1441.18289 149.0416 328.2854291
dWfront In rebound -1441.1829
dWrear In jounce 1441.18289

C.G. location:

Locating C.G. mm
a\' distance from front axle. 1369.06
b\' distance from rear axle 1120.14

Deflection with zero compensation(function of wheel rate and load transfer):

Deflection due to dynamic loading \'Z\' considering zero \'Anti\' characteristics mm/g mm in/g
Zfront in rebound 1.65883806 16.04042 0.631512444
Zrear In Jounce. 1.2795738 12.37306 0.487128189
Pitch angle Degrees degree/g radians
θ 0.6543175 0.06766993 0.011415
Pitch gradient 0.011415 0.001180465

Dynamic load transfer as per drive configuration of vehicle:

Calculating \'Anti\' characteristics:

Front axle:

I.C. Location and \'Anti\' properties considering a \'Solid axle\' suspension mm radians degrees Ratio
Front end: e\' 335.788 0.46386
d\' 723.9
Front \'Anti-lift\' angle [θf]actual 0.43432 24.8973
For 100% anti lift swing arm angle [θf]ideal 0.17176 9.846123
Front \'anti-lift\' %, ([θf]actual/ [θf]ideal)*%front*100 0
100% RWD vehicle will have zero torque reaction forces at the front

Rear axle (for an independent rear suspension):

I.C. Location and \'Anti\' properties considering a \'Independent rear\' suspension
Rear end: e\'=\'e-wheel radius\' 114.3 0.105882
d\' 1079.5
Rear \'Anti-squat\' angle [θr]actual 0.105489 6.047158
For 100% anti squat swing arm angle [θr]ideal 0.17176 9.846123
Rear \'anti-squat\' %, ([θf]actual/ [θf]ideal)*(Driverear)*100 61.03806

Designing for Zero pitching:

3. Zero pitch condition (100% pitch compensation)
Rear end: e\' fixed 406.4
e1\'=\'e-wheel radius\' 114.3 0.424036
for zero pitch, Zfront = -Zrear. Rear \'Anti-squat\' angle [θr]actual 0.401054 22.99036
Hence,
[dWfront(h/l) - (dWfront(e/d))*Drive ratio front] /Kfornt = - [dWrear(h/l) -dWrear(e/d)*Drive ratio rear] / Krear
where, dW(h/l) is the dynamic load, and dW(e/d) is the \'Anti\' characteristics force.
for 100% RWD vehicle,
[dWfront(h/l)] /Kfornt = - [dWrear(h/l) -dWrear(e/d)*Drive ratio rear] / Krear
Now,
(Krear/Kfornt) = [-(h/l)+(e/d)] / (h/l)
0.424036281
958.4086
d1\' for 100% pitch compensation, 269.5524
Rear \'anti-squat\' % (for 0 pitch), ([θf]actual/ [θf]ideal)*(Driverear)*100 244.4444
Front \'anti-lift\' %, (for zero pitch) ([θf]actual/ [θf]ideal)*%front*100 0
100% RWD vehicle will have zero torque reaction forces at the front hence, even in the 0 pitch condition all the forces are transmitted through rear suspension links and hence the 244% anti-squat.

Deflections at the axles for 100% pitch compensation:

Deflection due to dynamic loading \'Z\' considering \'Anti\' characteristics(244% anti-squat) mm in/g
Zfront = [dWfront(h/l)] /Kfornt in rebound

mm/g

1.91628973

18.52989 0.729523176
Zrear = [dWrear(h/l) -dWrear(e/d)*Drive ratio rear] / Krear (-) in rebound -0.1326662 -18.5299 -0.05050545
Pitch angle 0 0

drive link to the excel sheet:

https://drive.google.com/open?id=1r7tWOIisKoi3O4IWf1OWscWiRP9-Ik-4

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