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

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.

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

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

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

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

Appendix

Appendix