Resultant Vorces and Moment (aircraft problem)

[clickcaptain]

Homework Statement

The directions of the two thrust vectors of an aircraft can be independently changed from the conventional forward direction within limits. For the thrust configuration shown, determine the equivalent force-couple system at point O. Then replace this force-couple system by a single force and specify the point on the x-axis through which the line of action this resultant passes. These results are vital to assessing design performance.

The Attempt at a Solution

I found the resultant force from the two thrust vectors

Fx = T + Tcos15
Fy = Tsin15

R = Fx + Fy = T*2.225

but after this I'm stuck on what to do, am i supposed to find the moment or set this equal to the moment?

 

[LowlyPion]

Homework Statement

The directions of the two thrust vectors of an aircraft can be independently changed from the conventional forward direction within limits. For the thrust configuration shown, determine the equivalent force-couple system at point O. Then replace this force-couple system by a single force and specify the point on the x-axis through which the line of action this resultant passes. These results are vital to assessing design performance.

The Attempt at a Solution

I found the resultant force from the two thrust vectors

Fx = T + Tcos15
Fy = Tsin15

R = Fx + Fy = T*2.225

but after this I'm stuck on what to do, am i supposed to find the moment or set this equal to the moment?

I think you need to assess the forces about the point "O".

You are given the dimensions of the points at which these forces act relative to O. There looks to be both a forward thrust and a moment associated with the result.

As to your first attempt, the force vectors will not add simply in the way that you have shown. (Besides the 2.25 looks to be calculated wrong in any event as you have managed to turn 2T of Thrust into 2.25T.)

 

[clickcaptain]

So do i need to calculate the moment about the point "O"?

 

[clickcaptain]

My plan of action was to find the resultant force and then set that equal to the moment

 

[LowlyPion]

So do i need to calculate the moment about the point "O"?

I think you need to calculate the contribution to the moment that is made by the forces about O.

There is of course the components of force that go to forward motion that will contribute to velocity. Those would be the X components - at least the ones that balance out against moment at O in the x direction.

 

[clickcaptain]

i have to keep the resultant forces broken up into Rx and Ry so how do i use that to figure out the moment?

 

[LowlyPion]

i have to keep the resultant forces broken up into Rx and Ry so how do i use that to figure out the moment?

Resolve the forces in the x-direction. The x-components of each create a moment about O acting on either side at a distance of 3M.

So you have 2 Thrusts of T*Cos15 that add together and point forward giving 2TCos15 forward thrust. You also have a clockwise contribution to moment about O of 3m*T - TCos15 or 3m*T*(1-cos15).

Figure then what the y-component does? What contribution does it make? What moment arm?