Brake Design Calculation for Sports Car and Racing Vehicles


Fundamental Assumptions for Steering and Brake:
·         Lateral and normal forces will be distributed equally on all wheels.
  • No lateral forces
  • No wheel compliance
  • No Body roll
  • Only front wheels contribute to steering
  • No suspension effects
  • No longitudinal weight transfers
  • Constant speed
  • No Air drag
  • Road has constant friction coefficient (Dry 0.8, Wet 0.3)

Vehicle Level Input Parameters:
Minimum (Car + Driver) Mass M = 545 Kg
Height of Centre of Gravity HCOG= 350 mm
Wheel Base Length WBL= 2700 mm
Front Centre to COG lm = 1900mm
Driver Weight = 75 Kg

Other Assumption:
Pedal Lever and Master Cylinder Efficiency=0.8
Bias Ratio = 0.8
Front/rear pad-disc brake factor = 0.76
Front and rear caliper cylinder efficiency = 0.98


D1, D2, D3, D4, D5 and V1 are iterations done by changing brake system component parameter value- brake diagram is made in next blog for each of these design iterations. In V1 iteration vehciel parameter were changed to check that basic vehciel design is OK or NG from the brake designer point of view. 

Brake Design Iterations
D1
D2
D3
D4
D5
1V*
Design Review 
Pedal Level Ratio
5
4
5
5
5
5
If Master Cylinder dia is increased, driver needs to apply more force to stop vehicle.
Master Cylinder Diameter mm
10
20
10
10
10
10
Front/rear caliper piston diameter mm
45
40
45
45
45
45
Mean effective radius of front braking disc mm
230
230
220
200
250
230
For bigger Disc, Driver needs to apply lesser force.
Mean effective radius of rear braking disc mm
220
220
220
200
250
220
Vehicle Parameters
Height of Centre of Gravity mm
350
350
350
350
350
300
*Vehicle COG, Wheel Base and Front Axle Location is changed for study.
Wheel Base Length mm
2700
2700
2700
2700
2700
2800
Front Axle to Centre of Gravity Distance mm
1900
1900
1900
1900
1900
2100
Driver effort to generate Actual Braking Force equivalent to vehicle weight (N)
To generate Normalized Actual Front Braking force equal to 1g
60
375
60
70
53
50
D5: At 1g driver need to apply only 53N to stop front wheel and 70N to stop rear wheel. 
To generate Normalized Actual Rear Braking force equal to 1g
75
325
75
90
70
75
Performance of Vehicle ( Different Driving Condition)
Maximum wheel unlocked deceleration ( Stable Design up to)
1 g
1 g
1.2 g
1.3 g
1.2 g
1.5g
Design 4 is most stable up to 1.3g line.
Optimal Front Force 0 at this deceleration (g) (X Intersection)
-2.28
-2.28
-2.28
-2.28
-2.28
-2.33

For further Improvement COG must be lowered, Wheel base need to be increased and COG shifted to rear wheel.
Optimal Rear Force 0 at this deceleration  (g) (Y Intersection)
5.42
5.42
5.42
5.42
5.42
7
Max deceleration during rear circuit failure with µ 0.8 Dry
0.25
0.25
0.25
0.27
0.27
0.2
Max deceleration  before front wheel  lock with µ 0.3 Wet 
0.2
0.2
0.2
0.2
0.2
0.18




 Conclusion: 

Design 5 will be used in vehicle because driver effort is least and vehicle is stable up to 1.2g line. As bias ratio is 0.8, rear brake will lock at higher force (70N) than required at front wheel lock (53N). If in physical test rear brake is locking then rear brake disc size will be reduced from 250mm.


Brake Pipe Design:  
Steel
Cu Alloy
Cu-Ni-Si Alloy
Remark
Lower Yield Strength  N/mm2
250
410
600
Though driver never apply full weight (75Kg) on brake. However system must be designed for worst case.
Pipe Thickness mm
3
3
3
OD mm
10
10
10
Burst Pressure in N/mm2 
150
246
360
Burst Pressure in Bar 
1500
2460
3600
#Pressure Generated by Driver Bar
212
212
212
Factor of safety
7
11.6
16.9


 (CU Alloy: Zirconium Copper Cold Drawn Aged; Cu-Ni-Si Alloy: Copper Nickel Silicon Aged)

Burst Pressure = 2 * Material Strength * Pipe Wall Thickness / Pipe OD
 #Conclusion:
Refer Design 5; A 75 Kg Drive (at 750N applied pedal force) can create up to 212 bar pressure in pipe with 10 mm Calipers piston, 45mm Master cylinder piston and Pedal Ratio 5. 


Brake Design Finalization :-

Total Mass Kg
Total Weight N
#Height COG
#Wheel Base mm
#Front Axle to COG
load on Rear Axle N
X
ψ
M
W (N)
HCOG
L  (mm)
Lm  mm
Frear
CG/WB
Frear/ W
545.0000
5346.45
350.00
2700.000
1900.0
3762.3
0.12963
0.70370
Rear calliper pushout pressure
Front/rear pad-disc brake factor
**Pedal lever ratio
Lever/master cylinder effici
Bias ratio
Master cylinder bore diameter
Master cylinder Area m2
**Front/rear calliper piston diameter mm
Por
Bff
Lp
np
Br
Dmm
Amc
Dcalpis mm
0.00000
0.76000
5.00000
0.80000
0.80000
10.00000
0.00008
45.00000
No of pistons in each front calliper
No of front callipers used
Front rear calliper cylinder effici
Mean eff radius of front disc
Radius of the front tyre m
**Front/rear calliper piston diameter m
Front calliper pushout pressure
Mean effective radius of rear braking disc m
nf
Nf
ncf
rf
Rf
Dcf
Pof
rr
2.00
2.00
0.98
0.25000
0.33
0.045
0.00
0.25
deceleration (g)
OPT F(N)
OPT R(N)
**Caliper Piston Area
0.00159



-3.30000
0.43389
-3.73389
Aplied pedal force (N)
ACTUAL F
ACTUAL  R
Pl F
Plr
-3.00000
0.27778
-3.27778
0.00000
0.00000
0.00000
0.00000
0.00000
-2.70000
0.14500
-2.84500
25.00000
0.47491
0.37993
707714.08351
566171.26681
-2.28570
0.00000
-2.28570
53.00000
1.00681
0.80545
1500353.85704
1200283.08563
-2.00000
-0.07407
-1.92593
70.00000
1.32975
1.06380
1981599.43383
1585279.54706
-1.80000
-0.11333
-1.68667
100.00000
1.89965
1.51972
2830856.33404
2264685.06723
-1.50000
-0.15278
-1.34722
125.00000
2.37456
1.89965
3538570.41755
2830856.33404
-1.20000
-0.16889
-1.03111
150.00000
2.84947
2.27958
4246284.50106
3397027.60085
-0.90000
-0.16167
-0.73833
175.00000
3.32438
2.65950
4953998.58457
3963198.86766
-0.60000
-0.13111
-0.46889
200.00000
3.79929
3.03943
5661712.66808
4529370.13447
-0.30000
-0.07722
-0.22278
225.00000
4.27420
3.41936
6369426.75159
5095541.40127
0.00000
0.00000
0.00000
250.00000
4.74912
3.79929
7077140.83510
5661712.66808
0.30000
0.10056
0.19944
275.00000
5.22403
4.17922
7784854.91861
6227883.93489
0.60000
0.22444
0.37556
300.00000
5.69894
4.55915
8492569.00212
6794055.20170
0.90000
0.37167
0.52833
325.00000
6.17385
4.93908
9200283.08563
7360226.46851
1.20000
0.54222
0.65778
350.00000
6.64876
5.31901
9907997.16914
7926397.73531
1.50000
0.73611
0.76389
375.00000
7.12367
5.69894
10615711.25265
8492569.00212
1.80000
0.95333
0.84667
400.00000
7.59858
6.07887
11323425.33616
9058740.26893
2.10000
1.19389
0.90611
425.00000
8.07350
6.45880
12031139.41967
9624911.53574
2.40000
1.45778
0.94222
450.00000
8.54841
6.83873
12738853.50318
10191082.80255
2.70000
1.74500
0.95500
475.00000
9.02332
7.21866
13446567.58670
10757254.06936
3.00000
2.05556
0.94444
500.00000
9.49823
7.59858
14154281.67021
11323425.33616
3.30000
2.38944
0.91056
525.00000
9.97314
7.97851
14861995.75372
11889596.60297
3.60000
2.74667
0.85333
550.00000
10.44805
8.35844
15569709.83723
12455767.86978
3.90000
3.12722
0.77278
575.00000
10.92297
8.73837
16277423.92074
13021939.13659
4.20000
3.53111
0.66889
600.00000
11.39788
9.11830
16985138.00425
13588110.40340
4.44444
3.87745
0.56699
625.00000
11.87279
9.49823
17692852.08776
14154281.67021
4.80000
4.40889
0.39111
650.00000
12.34770
9.87816
18400566.17127
14720452.93701
5.10000
4.88278
0.21722
675.00000
12.82261
10.25809
19108280.25478
15286624.20382
5.42857
5.42857
0.00000
700.00000
13.29752
10.63802
19815994.33829
15852795.47063
5.70000
5.90056
-0.20056
725.00000
13.77244
11.01795
20523708.42180
16418966.73744
6.00000
6.44444
-0.44444
750.00000
14.24735
11.39788
21231422.50531
16985138.00425

Please go to next blog to understand above brake design graph. Each and every parameter is plotted on brake design diagram for different iteration and best is selected. please go next blog for final brake design.