# Propeller thrust in restricted air flow environment

• B
houlahound
looking at where to start understanding how the thrust/lift generated by a specific propeller (hypothetical one) changes as a function of surrounding air pressure.

obviously the lift will go to zero as air pressure decreases.

as pressure increases, modelled by say mounting the propeller inside a sealed air chamber not much bigger in diameter than the propeller diameter and say 10 times the volume, how is lift effected and why?

no specific calculation required, just trying to get my head around the physics.

thanks any replies.

## Answers and Replies

Ion Aguirre
Hi Holulahound:
That's not a question of presure, but of density. Air is a compressible fluid, hence, density is not constant with pressure. Thrust and Torque of a propeller are directly related to density. Hence, when pressure changes, density changes as well and then, Thrust and Torque do the same.

Regards

• houlahound
houlahound
That Ion, I expected a change, can you link me to any relevant math?

Ion Aguirre
Hi Houlahound
We have no perfect propeller mathematical model by now. Anyway ....some notes ...

Propeller thrust at working RPM:
T= Kt dens N^2 D^4

Required torque at working RPM
Q= Kq dens N^2 D^5

Kt and Kq are experimental coefficients
dens --> fluid density
N ------> Propeller rotation rate given in Herz N= RPM/60
D -----> Propeller diameter

Efficiency is given by the relation between input and output power (Power consumed by the propeller and power delivered)

eff= T V/(2 PI N Q)

Although there is no perfect model,my advice is that having a look to the "Blade Element Momentum Theory" could be a good starting point for "grabbing" the key concepts about how a propeller works.

For an approach to air density at given conditions, the Ideal gas equation can be used: dens= (P M)/(R T)
Where:
P --->> Pressure
M --->> Molar mass (Air is a mixture not a single element --- Use any standard)
T -->> Absolute Temperature
R -->> Ideal gas constant (Value will depend on units)

Dont hersitate asking again if needed.

Regards

• houlahound
houlahound
Thanks great starting point, I will look into it.

I am building a racing drone at this very moment, going to use the free download flight control software and some load cells to measure the bejesus out of it.

Spare time project, expect to get results possibly this year.