Hi All
Lately I have been analysing chassis from a static point of view and have noted something very odd about the DJI chassis. For the asking price of 1000$-2000$ I felt very naive at first. I then started to analyse the copter from a statics points of view and there is one point(the inclination of the arms) I need clarification on:
Assumptions:
* Hover State
* Symmetrical Physical Structure
* All motors are at the same throttle level(This produces a force F_x)
* Sum of moments=0 (Dynamic equilibrium)
* Axis convention per figure
Problem: The inclination of the arms when maintaining static equilibrium:
To begin with to maintain static equilibrium the sum of force about the x and z-axis must be zero.
ie. Sum(F_x)=Sum(F_z)=0
To bring my point across I will look at a symmetrical section, analysing two arms only:
The force along the X_b axis will cancel maintaining equilibrium along the X_b axis.
The problem comes in when the component of the force along the Z axis apposes the weight vector.
ie. 2(F_x cos(THETA))=mg
As apposed to a completely horizontal arm: (THETA=0)
ie.. 2F_x=mg
I hope some one can provide clarification to the above as to why the inclination of the arms. Duly noted that this will have and effect of endurance.
Regards
Replies
I'll take a wild stab that this acts like dihedral on plane wings in level flight - it will naturally try to self-level if left to it's own devices, at the expense of maneuverability and downward thrust. But I imagine the payoff is pretty small, and I'm massively over-generalising!
Note: auto-self-leveling is a bit of wishful thinking in MR's, especially if altitude or position hold are requirements. Yeah, it'll probably do it but the tolerances will be tiny, the PID rates will be massive, and your alt control and X/Y control will be nil.
Small update on S1000:
Each frame arm is designed with an 8° inversion and a 3° inclination, making the aircraft more stable when rolling and pitching yet more flexible when rotating.
As Phillip mentioned the angle is there mainly to aid stability. Another example where this principle is used is in the rockets used to launch the shuttle. The thrusters are at a slight angle to aid stability at the expense of a slight loss in upwards thrust.
The arm inclination is for natural roll/pitch stability and to provide additional clearance so that the arms/motors/props are sure not to intrude into the line of sight of a camera system. It is slightly less efficient than flat arms, but not to a significant degree.
I figured Fx sin (theta) is a waste of a thrust vector. :)
Seems like your smarter then anyone here. Bump looking for an answer as good as the question.