Restrictor

The restrictor is a part of the intake that provides a ceiling for power of the student vehicles in the competition. The theoretical upper limits of the engine's power can be derived to be in the ballpark of 100-110hp depending on many factors.

Some teams claim to have measured power figures above this level, do not use this page to attempt to disprove these claims. Do not copy this page for use in the design review, the assumptions are unjustified. The calculation here is wrong at best and misleading at worst.

Power Limit Derivation

The upper limit is derived using the general equation for ideal compressible gas flow:

A	Area
R	Gas Constant
Tt	Total Temperature
$\gamma$	Specific Heat Ratio
M	Mach number
Pt	Total Pressure

${\dot {m}}={\frac {A*p_{t}}{\sqrt {T_{t}}}}*{\sqrt {\frac {\gamma }{R}}}*M*(1+{\frac {\gamma -1}{2}}*M^{2})^{-{\frac {\gamma +1}{2(\gamma -1)}}}$
when M becomes 1, the flow is considered choked. The equation becomes:
${\dot {m}}={\frac {A*p_{t}}{\sqrt {T_{t}}}}{\sqrt {\frac {\gamma }{R}}}(1+{\frac {\gamma -1}{2}})^{-{\frac {\gamma +1}{2(\gamma -1)}}}$
With some basic assumed values at sea level, the maximum mass air flow through the restrictor can be found:

A	3.14 e-4	m2
R	0.286	kJ/kg-K
Tt	300	K
$\gamma$	1.4
M	1
Pt	101.325	kPa

Plugging these into the equation above yields a steady state mass flow rate of 0.074 kg air per second for a 20mm restrictor. A 19mm hole allows 0.067 kg/s of air. Some ball park power limits can be found as follows:

Gasoline
If we assume an AFR of 13.1 (typical lambda for high torque for NA engines[citation needed]), and a Q_LHV of 43.4 MJ/kg , the mass air flow yields a power limit of 245.1 kW or 328 hp total energy output. If the thermal efficiency of the engine is assumed to be a nominal 33%, the maximum available mechanical power is 81.7 kW or 109 horsepower with 100% volumetric efficiency.

E85
Using an AFR of 8.7 for E85 and a Q_LHV of 29.2 (citation needed, this was just .85*qlhv ethanol + 0.15 * qlhv gasoline), the limit is 248 kW or 332 hp. The available mechanical power assuming the same efficiency as above is 75.0 kW or 98.5 hp. There are more complexities to using e85 such as the cryogenic effect of fuel vaporization leading to a denser charge, but that is out of the scope for this specific ballpark calculation

This limit could be exceeded by increasing the upstream pressure to greater than 1 atmosphere. In FSAE, any compressor must be placed after the restrictor so this is not possible.

Assumptions

• The air flow is smooth
• The air flow cannot go supersonic
• There is no friction in the intake system
• The intake restrictor is exactly the maximum allowable size.
• The volumetric efficiency of the engine is 100%

Factors to Consider

Mach Number vs Mass Flow Rate

• What is the effect of the pulsed nature of engine air flow? Is the impact of the pulsed flow consistent throughout the engine's operating range?
• what is your actual volumetric efficiency?
• are you operating at Mach # = 1 at all points in the race?
• what is your restrictor's discharge coefficient?
  • well designed venturi style restrictors can see Kd as high as 0.95 [citation needed]
• is your engine operating at 33% efficiency? that is a rough rule of thumb

Component Design

• Diffusion angle
  • intake angle
  • output angle
• Surface roughness
  • Boundary layer adhesion
• Length
• Material
  • Construction
• Support