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:
* 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.
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)
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.
Seems like your smarter then anyone here. Bump looking for an answer as good as the question.
I figured Fx sin (theta) is a waste of a thrust vector. :)
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.
Hi Phillip please can you explain the how the pitch and roll stability is improved?
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.
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.
As it already has been noted below, this basic concept for natural stability is not native to MR.
Here's basically how it works:
A force causes the MR to pitch and or roll. As this happens, one side will will approach level which will both increases the effective moment arm while also bringing the thrust vector perpendicular to the ground. This will maximize the moment produced by this side of the MR. The opposite side of the MR will rotate up which will reduce it's effective moment arm while also reducing it's vertical component of thrust. Both of these effects combined reduce the high side's effective moment. The net result is that the MR will try to rotate back against the direction of disturbance.
This strategy is not intended to replace the active stabilization produced by the controller, but to augment it. In flight based video, there is a high value placed on platform stability, so the trade-offs are not an issue. This would be a sub-optimal design for someone who wanted to absolutely maximize either flight time or maneuverability.