1. Analytical Model of the Cooling System of a Formula SAE Race Car
By:
Dave McClelland
Jacob Zuehl

2. Background Objectives
The cooling system removes heat from the engine and maintains it at its optimal operating temperature. If the engine becomes too hot, the engine will produce less than optimal power and risks permanent damage. In the past two years, the cars have not had adequate cooling. There was no analytical model to aid in the design of the cooling system.
Objectives
Produce a simplified analytical model of the cooling system as a basis for future years.
See how changes in various parameters affect the air speed required.

3. Problem Setup Establish Governing Equations
Assumptions: Steady State, Conduction=0, Vair=Vcar

4. Results Select Design Parameters of Interest
• Number of Radiators
• Fin Air Channel Size
• Engine Heat Load
• Ambient Air Temperature
Examine Effects of Each Parameter
• Vary one at a time
• Calculate the required airflow speed

5. Results Varying the Number of Radiators
Varying the Fin Air Channel Size
Number of
Radiators
Required Air
Speed (mph)
Required Fan
Load in Idle (CFM) 1
58.6
2593.8 2
30.9
1367.7 3 10
442.6
Fin Air Channel Height (mm)
Required Air Speed (mph)
1.0
7.8
1.495
30.9
10.0
187
Varying the Engine Power Output
Varying the Ambient Temperature
Heat Load (W)
Required Air Speed (mph)
14914
6.5
24857
30.9
37285
43.3
49713
65.3
74570
121
Temp. of Ambient Air
Required Air Speed (mph) 60 23 75
30.9 90
32.7
100
35.8

6. Conclusions & Recommendations
It is confirmed that the cooling system on the current car is not adequate
The model should be verified by measuring inlet and outlet temperatures of the air and water and mass flow rate of water
A relationship between air flow through the radiator and vehicle speed should be determined
Changes from a straight shroud should be considered
Measure fuel usage during average driving to better approximate heat rejected

7. Appendix

8. Appendix