#### Background

From Brunt et al^{1}:

- Gamma (γ) is the ratio of specific heats. A low value of gamma produces heat release value that is too high and a heat release rate that
is negative after the completion of combustion.
- A temperature dependent equation for gamma is produced from experimental data:

`gamma=1.338-60*10^(-5)T+1.0*10^(-8)T^2` (Equation 1)
- Gamma is also dependent on equivalence ratio, Φ. The effect of ignoring this term is an error of up to ±0.015 in gamma (0.8<Φ<1.2)

Hayes et al^{2} and Rocco^{3} present Zucrow and Hoffman's equations of gamma:

`gamma=(bar C_p)/(bar C_p - bar R)` (Equation 2)

for T < 1000K

`bar C_p=(3.6359-(1.33736T)/1000+(3.29421T^2)/(1*10^6)-(1.91142T^3)/(1*10^9)+(0.275462T^4)/(1*10^12))bar R` (Equation 3)

for T > 1000K

`bar C_p=(3.04473-(1.33805T)/1000-(0.488256T^2)/(1*10^6)+(0.0855475T^3)/(1*10^9)-(0.00570132T^4)/(1*10^12))bar R` (Equation 4)

The main advantage of temperature dependent gamma is that it adjusts to different engine operating conditions - higher values of gamma would be used at low engine load.

#### catool

The following calculations are made available in catool:

- GAMMA - Crank angle based gamma curve

catool Implementation: See Return_Gamma_Data() in analysis.c

#### References

1. Brunt, M. F. J., Rai, H., Emtage, A. L., "The Calculation of Heat Release Energy from Engine Cylinder Pressure Data," SAE Paper 981052, 1998.

2. Hayes, T. K., Savage, L.D., "Cylinder Pressure Data Acquisition and Heat Release Analysis on a Personal Computer," SAE Paper 860029, 1986.

3. Rocco, V., "D.I. Diesel Engine In-Cylinder Pressure Data Analysis Under T.D.C. Setting Error," SAE Paper 930595, 1993.