# Thread: Complicated Maths Problem!...Long Shot...

1. ## Complicated Maths Problem!...Long Shot...

Hi all, Im trying to track down a formula which I know DOES exist because I used to know it! And I cant find a record of it :ARRGGG: or find the guy who told me it in the first place a few years ago!

I know this is a long shot since it ain't directly related to this site, but the guys on the physics forum haven't been much help yet!

Anyway, I need to calculate THRUST REQUIRED to lift a given object vertically off the ground using a propeller when I have a set of known values. My known values are:

Object Weight
Object Drag Co-Efficient
Prop Diameter
Prop rpm
Prop Pitch
Air Density
Gravitational Force

Therefore:
Thrust Required = Above values combined somehow!

Im not holding my breath but thanks for any help. I've been looking for this now for a little over a month. I even have other people not on the internet trying to find it for me without any joy. From memory it included all of the above values 'except' the prop pitch, but my memory is a bit vague. BUT IT DOES EXIST.

2. Originally Posted by diarmaid
....Anyway, I need to calculate THRUST REQUIRED to lift a given object vertically off the ground using a propeller....
The thrust required to lift any given object vertically against gravity is just a bit more than the object's weight; no formula needed for that.

3. Thanks Geof. But that wont work. Its possible that Im mixing up my formulas and constants. So I know the force in Newtons required to push up from converting the weight to Newtons pushing down. But I need to generate the upward force using my constants above. I put in my prop factors, the drag coefficient, the force in Newtons pushing down and the air density. then I get my required value...EUREKA...in POUNDS OF FORCE REQUIRED TO MOVE THE OBJECT. I think the result was pounds of thrust which I could then convert into hp to determine the necessary engine size.
There is definately a formula for this somewhere....Im getting more confused about this every day....

5. Im thinking about the above post and Im nearly sure from memory that its somewhat correct. Using the constants:

Prop Diameter
Prop Pitch
Prop rpm
Air Density
Drag Co-Efficient
Speed

I can determine the thrust in pounds given off by a specific prop which I can convert into Newtons and back calculate to get the required prop in order to generate the required thrust to overcome the weight, then use the pounds thrust values to calculate the necessary horsepower of engine. Is this even vaguely making sense. Its very hazy in my memory.

6. GENGUY, YOUR A GENIUS!!! I can't be certain at this point but Im 80% sure that this was my formula:

Cr = T / p . n2 . D4

Thanks a million. I'll let you know if this is the right one or not after I've tested it out.

Edit: Damn cnc zone is Great! Stupid physics forum, won't bother asking a question there again!!
I knew it was a simple formula, just couldn't remember the darn thing!

7. Wait a minute......In the above formula the Thrust is given by the value 'Cr', but the value 'T' also represents thrust. Im assuming that both are Newtons and that the value 'T' is the required thrust, and 'Cr' the....what exactly??

8. Originally Posted by diarmaid
Thanks Geof. But that wont work....
Oh yes it does. The force of gravity on any mass is its weight. The minimum thrust needed to just counteract the force of gravity is equal to the object's weight. In order to give the object an acceleration upwards the thrust must be greater than the object's weight. The magnitude of the acceleration depends on the object's mass according to the equation a = F/m (acceleration = thrust divided by mass). Once you have a nonzero upward velocity then you start considering aerodynamic drag on the object.

9. lol. Thrust you to start a good 'discussion' Geof! Your right of course. I meant that it wont work for me in the context of what I need to establish. The physics guys have started posting replies on the other site aswell and now I have 6 formulas after over a month of pulling hair out from this!! lol Should have asked first then gone looking. In post Number 7 above I made a mistake. 'Cr' is the required thrust, and T is the what exactly, any ideas?

10. There is another real simple one that might work:

u = F/N

Where:
u = coefficent of friction (actually 'mu')
F = Force you're looking for
N = Force that the body exerts Normal to the plane of support. Pretty sure that N has to be in Lbs mass.

If you lump the drag factors into a combined factor (tire friction, parasitics, and/or aero drag), I'd guess that you could call this your "coefficient of friction".

The other two are then readily measured and/or solved for.

11. Originally Posted by diarmaid
GENGUY, YOUR A GENIUS!!!
Nope, no genius here, just good at googling the answers!

Originally Posted by diarmaid
Wait a minute......In the above formula the Thrust is given by the value 'Cr', but the value 'T' also represents thrust. Im assuming that both are Newtons and that the value 'T' is the required thrust, and 'Cr' the....what exactly??
The italics make it a bit hard to read. It is Thrust Coefficient - Ct not Cr.

12. Originally Posted by diarmaid
... in the context of what I need to establish....
Just what are you trying to establish? Your first post said you want to calculate the thrust to lift an object. However, now I think you do accept that the thrust needed is actually the weight. So are you looking to calculate the power required with a propeller that has particular characteristics, or the rpm, or the efficiency?

Incidentally don't talk about Newtons and pounds in the same sentence; they are both units of force just in different measuring systems.

Also Cr is not Cr it is Ct and it is the Thrust coefficient. I have a feeling the link genguy gave is not going to help because it seems to be discussing comparisons between propellers using dimensionless coefficients.

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