Hi again, Breadboard:
Breadboard said:
Anyway, I need to calculate the values for the object to rise vertically from a stationary position at ground level. Not in flight with lift generated by lift surfaces.
Ahh, OK I see. Then the Treq=Drag equation I provided is not applicable. In fact, if you are lifting it vertically then only drag upon the body underneath the propeller is relevant, and it would be acting in the same direction as weight. You can use the same drag equation I gave you, but just drop the "=Treq" part. This drag force would be added to the weight that you would have to overcome.
1) In your formula above Treq = Drag = CD*0.5*rho*Airspeed^2*(Aircraft Wing Reference Area) what does the value 'CD' represent please?
That would be the drag coefficient which you said was a given. To use this equation given the vertical lifter you describe above, you would have to replace Airspeed with the exit velocity of the propeller (which you refer to in a later equation). And instead of the wing reference area, you would need to know the frontal projection area of the body underneath the propeller, as this would be the area used to arrive at the non-dimensional drag coefficient.
2) The prop pitch varies from hub to tip, but when purchasing they have a given pitch value, can this value not be used to give a relatively accurate approximation for the prop?
In that case, the manufacturer of the prop is typically quoting you the pitch of the propeller blade at a distance 75% of the way from the hub to the tip. You MAY be able to use this along with the thrust coefficient, but I am going to have to think about how...
The other formula I have come across is:
Ct = T / p . n^2 . D^4
Where:
Ct = Thrust Co-Efficient
T = Thrust
p = rho
n = rev per sec
D = Diameter
3) I think this formula is more appropriate however I don't know what 'Ct' or 'T' are measured in. T would undoubtedly be Newtons but 'Ct' ?
'Ct' is a dimensionless coefficient, just like the drag coefficient. If you check the dimensions you will see that Ct turns out with reduced units of "1/rev^2", which is essentially non-dimensionalize to the inverse of the square of the rotational rate of the prop.
4) And what's the relationship between them so far as the difference between T and Ct? ie: How do I calculate Ct?
Just like an airplane manufacturer specifies the drag of a specific airplane design by the drag coefficient (CD), a propeller manufacturer will quantify the thrust performance of a specific propeller design via the Ct. Therefore, Ct should be a number specified by the propeller manufacturer for any given design. You then scale it to the thrust you need by making it larger (D) or making it rotate faster (n). This is why I believe you should be able to use the pitch factor along with the Ct. For a given blade pitch, the manufacturer should be able to tell you what the Ct is for that specific propeller design (with the noted amount of pitch at 75% of the blade radius).
I also found another formula that I think is not what I need, but it could be relevant. Its:
F = .5 x r x A x [Ve^2 - Vo^2]
Where:
F = Thrust
r = Air Density
A = Prop Disc Area
Ve = Exit Velocity
Vo = Aircraft Velocity
This is the standard propeller equation which relates the force produced by the propeller to the difference in airstream energy (velocity^2) between in front of the propeller (Vo) and behind the propeller (Ve). This difference in velocity is tied directly to a specific propeller design (Ct and the pitch).
5) My major problem with this formula was that I couldn't figure out the value for Ve. Any ideas?
This is directly related to the aerodynamics of the propeller (pitch and Ct) and what rotation rate it is turning. If you were given a Ct by the manufacturer (for the specific pitch), then you could solve the Ct equation for "T" and set that equal to the "F" of this equation. If you then assume Vo=0 (you are hovering with no axial airspeed approaching the propeller), you could then solve this equation for Ve.
6) Last but not least, I am going to be using either a 4 or a 5 bladed propeller. How does this change my formulas if at all? I am thinking that for example with a four bladed prop I would just double the resultant thrust. Or would I have to increse my powers in the formulae by a factor of two? (ie: ^4)
It is not that easy. Propeller thrust does not scale linearly with number of blades... mostly because of aerodynamic interference effects between the blades. The aerodynamic force created by one blade creates the dreaded "downwash drag" on the propellers behind it. Depending on the aerodynamic design of the propeller blade itself, adding blades could actually create more drag and thus be less thrust. This is where "simple" propeller design assumptions break down and computational fluid dynamics and differential equations are needed to accurately model and analyze the propeller flowfield.
I would not worry about trying to model the effects of multiple blades. That is too detailed for what you are doing. All you really want to "tailor" is the velocity difference from front to back of the propeller shown in your "F" equation above. It should be as large as you need to lift your weight (and oppose the drag the propeller creates) but no larger. The reason is that when you analyze propeller efficiency, it (prop efficiency) actually goes DOWN (becomes less efficient) as the difference between Vo and Ve goes up. This is generally why propellers are not used for aircraft that have to fly at Mach numbers above about 0.6 because their efficiency is poor compared to turbofan jet engines.
Rainman
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