# Is there a formula to convert SFC to air-fuel equivalence ratio λ?

Speaking about aviation internal combustion engines, is there a way to get the current value of air–fuel equivalence ratio (λ) given current specific fuel consumption (SFC) and current power?

Is the relationship between SFC and λ fixed or does it vary with engine displacement and/or power?

The data I currently have is:

• The engine SFC at best power as watts/Kg*sec
• The current engine power output in watts
• The current engine fuel flow in Kg/sec
• I know that λ is about 0.85 when SFC ratio is about 1 (best power)

No, there is no formula to calculate the air-fuel equivalence ratio from specific fuel consumption (SFC). To calculate the equivalence ratio, you need the air mass flow, and the fuel mass flow. From this data, you can calculate the actual AFR (air fuel ratio), and lookup the stoichiometric AFR for your given fuel.

$AFR = \frac{m_{air}}{m_{fuel}}$

The air-fuel equivalence ratio is then simply calculated from these two AFR values.

Air-fuel equivalnce ratio: $\lambda = \frac{AFR}{AFR_{stoich}}$

You don't have a value for the air mass flow. You only have fuel flow from the SFC and current power.

If you had the equivalence ratio and SFC at two different operating points, not just one, you could assume linear interpolation, or extrapolation, to the SFC in question.

With the equivalence ratio and SFC at just one point, you would have to find a characteristic curve for SFC vs equivalence ratio for a similar type of piston engine and the same fuel type, and assume the shape of this curve is applicable to your particular engine.

• What if I know the engine displacement, compression ratio and the air density? I could get the air mass that way? – SeeEn Dec 6 '17 at 10:41
• @SeeEn. You would also need the rpm to get a mass flow from displacement and rpm. This probably assumes 100% replacement of the air every stroke. So it would be an approximation, not sure how rough. – Penguin Dec 6 '17 at 10:52