Maybe you are one of those who googled for the difference between Quadcopter & Tricopter. For sure you found many feedback and comparisons.
Mainly the difference will be regarding power consuming, or mechanical complexity. Some prefer Quadcopters for its simplicity to build and fix, others prefer TRICopter for its ability to YAW more aggressively.
In this acticle we will discuss deep differences between Quadcopters & Tricopters, and the point here is flying & stability equations difference between quadcopter and Tricopter.
First Lets discuss Quadcopter Equation - no details here just a fast review-:
more details in broken english is here
There are three core equation for Stabilizing & Flying quadcopter is:
assuming M1, M2, M3, M4 are thrust for each motor.
Thrust(M1) + Thrust(M2) + Thrust(M3) + Thrust(M4) = Total Thrust ... and this is determined by Thrust Stick only.
Thrust(M1) + Thrust(M3) = const. ... determined by Thrust stick equation #1
Thrust(M2) + Thrust(M4) = const. ... determined by Thrust
so for example when you want to roll anti clockwise, you increase M2 thrust by x and decrease M4 thrust by x. so that Equation 2 is always Valid under the same Thrust Stick position.
So for a roll a typical equation is:
M2 = Thrust + StickRoll * factor + PID (IMU ROLL)
M4 = Thrust - StickRoll * factor - PID (IMU ROLL)
so what you add to a motor is substracted from the other one on the same bar. That is because we need to keep the third equation valid:
Moment (M1 + M3) = Moment (M2 + M4)
This is very important because this is HOW QUAD make and correct YAW. Quadcopters -hex & octa- correct YAW using moment difference between motors on different bars.
So when we want to Roll equations are:
M1 = M1 + Stick YAW * factor + PID (IMU YAW)
M3 = M3 + Stick YAW * factor + PID (IMU YAW)
M2 = M2 - Stick YAW * factor - PID (IMU YAW)
M4 = M4 - Stick YAW * factor - PID (IMU YAW)
What you can notice here from above equations is that no equation CONTRADICTION with the other two. Ideally of course, as in real world we make some assumptions:
1- thrust is linear with motor signal sent to ESC - which is false but works :) -.
2- motor response to signal change instantly, so we read the very last IMU signal and send correction. especially if we use P only no I or D, we read the only last value, which is not true as it may has nothing to do with the last change because of inertia of propeller, quadframe ...etc. but again it works :)
Now lets go to Tricopter
The following equations are used:
Thrust(M1) + Thrust(M2) + Thrust(M3) = Total Thrust ... and this is determined by Thrust Stick only. same as quadcopter.
Thrust(M1) + Thrust (M2) = const for ROLL
but wait. Motor M1 & M2 acts as one virtual motor with M3 for pitch stabilization.
so Thrust (M1 + M2) = virtical Thrust (M3) = Thrust (M3 ) * Sin (ceta)
This is OK as for Roll we add x for M2 & subtract same x from M1 and it will not affect the pitch stabilization -at least in theory-.
Now lets go to the equation of YAW:
Moment (M1) + Moment(M2) = Thrust (M3) * Cos (ceta)
to correct or make YAW motion, you need to change ceta of Motor 3 using the Servo. But wait This will affect equation #2.
changing ceta will not only correct the YAW but will corrupt the pitch balance in equation #2, and then thrust of M1, M2 & M3 needs to be corrected
again to correct the picth. but wait this will corrupt equation #3 because the YAW will be affected again and again in infinite loop :)
So if you correct YAW using Motor thrust angle, and correct Picth using M3 Thrust then equation #2 & #3 will affect each other, but the Tricopter will be balanced as a whole, because correction is so fast and accurate especially when using a digital servo.
THERE IS A BIG difference between Quadcopter & TriCopter in flying concept.
The main advantage I can find in Tricopter because of the Servo:
1- You can get more agressive YAW motion compared to Quadcopter, as Thrust is used for YAW not moment, and thus force for YAW control can be higher.
2- You do not need to care about CCW & CW props as long as motors & their props rotates in the right direction, the servo will correct any moment even if all motors are CW or CCW. does not matter.
Best of All is Tilt motors for Racer FPV:
in Quadcopter if you fly in X mode and made front motors tilted to gain speed while keeping the frame horizontal for better aerodynamic.
In this situation the Roll correction will YAW deviation because thrust vector is not vertical to frame and when one motor corrects the Roll by increasing thrust it will cause YAW motion because of thrust horizontal component.
Things will be worst if the same motor is used to correct YAW using moment in the opposite direction, then YAW will not be stabilized at all.
in Tricopter this will not happen, actually you can build a fast Tricopter with tilted motor, and just ignore this effect, because YAW correction happens by the third motor servo, and equations 2 & 3 already affect each other, and will actively stabilize.
I do think it is important to note that the only reason tricopters with the same total swept prop area as an equivalent quad are more efficient is because of the larger prop diameter in the 3 propellers of the tricopter to acheive the same swept area as the four propellers of the quad.
For the simple reason larger diameter props are intrinsically more efficient than smaller ones.
@ Andrew, Even given that the servo, especially under competition conditions, and especially if always on digital is going to be drawing significant current (More than a GPS - a lot more) and this loss cannot be simply discounted, the weight is not what is important, the power draw is.
The only real issue is does the irretrievable loss in the servo operation get made up for by the increase in prop diameter for equivalent swept area.
I would suspect under some flight conditions it does and under others it doesn't.
And the servo and it's attendant mechanical implementation method do represent a structural and failure prone weak link on a tricopter, especially in "mishaps".
Basically I am in agreement with Leonard, although I think that wwith a streamlined appropriate shell a case can be made for forward prop tilt for high performance copters, Quad or Tri.
And as he said, just line up the flight controller (IMU) with the horizontal prop Axis and even existing ones are pretty much self compensating.
Of course, the IMU could be offset in firmware as well.
I have been flying a tricopter with Arducopter for about 4 years doing mapping and have had no tuning problems. Tricopters seem to be easier to keep orientation for some reason. I agree on the efficiency, with 2D flat map gimbal and canon s110 I get ~30 min on 4s 8000mah. The weak link for me is the servo. I use a large and fast metal gear digital on the rear when running a 14 inch prop using MK motors. I have had to replace two due to slop in the gears. Wish Arducopter would add a Y4 configuaration. Good discussion, guys.
There is a lot of information here, some correct, some incorrect.
Tri-copters are more efficient for the same prop area unless the designer is doing something silly.
Tri-copters provide good yaw performance ONLY if the CG of the rear motor and prop is below the pivot point.
Tri-copters yaw performance (assuming perfect setup) improves over a multirotor on larger copters. Servoes are not fast enough to copter with esc speed on smaller frames.
Tri-copters suffer terribly from cross coupling between roll/pitch/yaw depending on propeller rotation direction, CG, tail CG. This results in a very sub optimal tuning meaning that overall performance is poor compared to a multi.
Tri-copters are a poor choice for racers because the yaw performance (and roll/pitch) isn't good enough and they are very delicate in comparison.
Tilting the propellers forward doesn't provide a significant benefit in speed or drag when compared to a well designed frame (QAV250 with tilted motors vs Alian or warp quad).
A quad with tilted motors does not have roll yaw coupling if properly setup (controller level reference is parallel to the rotor disk). In short, if you tilt the motors tilt the controller.
Tri-copters win for a simple compact folding design. Y6 can get close but the lower props make landing without ground strike problematic. Having said that to get good yaw performance on a tri you generally need the rear prop on the bottom. My preference for a compact travel quad is a folding quad.
Feel: Personal opinion isn't really relevant to an engineering discussion (assuming this is an engineering discussion) but my personal opinion is tri-copter yaw feels terrible in comparison, loose, slow, and terribly cross coupled with the other axis. But as I said, my opinion on feel isn't really relevant.
Cost: I think this needs to go to the quad.
A couple of quick points on the state of the Arducopter code:
Tri-copters have not been well looked after and there needs to be some code added to bring the motor mixing up to the same standard as the multi-copters. This will mean the yaw/pitch coupling will be improved and tri-copters will have better use of the full throttle range.
Multi-Rotors have had the yaw controller dramatically improved in the last release. Until now multi-rotor controllers have neglected the inertia of the motors and props in the yaw controller. By including the motor inertia, yaw control on multi-rotors has been dramatically improved!!! This means yaw control is now much more direct and powerful.
Conclusion: Tri-copters loose in all but efficiency and easy folding.
Gary, I disagree about efficiency.
I think we can agree that, generally, a bigger prop and a bigger motor provides better effciency, so let's take that out of the equation. Let's only compare a tri-copter setup and a quadcopter setup of equivalent lift.
A 9 gram servo might be a factor in a micro drone, but at the 500 size a 100mAh servo is certainly not a factor. The servo's power usage depends on how much you're maneuvering but let's stay within practical limits, its energy consumption is on par with the GPS and other electronics. In a normal setup there is very little load on the servo.
A higher number of motors generally reduces efficiency due to obvious factors. A traditional helicopter is one of the more efficient setups. That said those differences are so small that they are easily lost in all of the other factors.
It is significant to note that in a quad copter, all four motors are providing propulsion for the amount of energy consumed.
In a Tricopter, the servo is a dead loss and a digital servos energy consumption is quite high.
Under roughly equivalent circumstance this means that a tricopter would have shorter endurance than an functionally identical quadcopter.
Further more, a strong case can be made for the servo being the least reliable component in the system.
Most servos are brushed and all feature an involved and sometimes inadequate gear chain (with losses and lash).
And a good brushless servo can arguably cost as much as an entire quadcopter.
And a tricopter represents a high load and high frequency application for a servo.
It is possible that if total swept area for the propellers was the same (tricopter would have bigger diameter props) that some of the servo power usage could be recovered by the increased efficiency of the larger diameter props.
And then there is the mechanical vulnerability of the pivoting motor mount.
Just a few additional thoughts to ponder.
I like how my tricopter responds to yaw input but I don't like to exaggerate. The autopilot code difference is minimal and the yaw feel is a minor concern to human pilots. When people ask me about tricopters versus quads I say in practice they're the same, tricopters are kind of easier to build with folding arms.
An important thing not mentioned for tricopters is the yaw "feel", only tricopter pilots (and maybe heli pilots) will understand the direct, solid, locked-in feel of a tricopter that makes any quadcopter feel mushy and loose. Another way to show the difference could be a co-axial heli (=quad) compared to a conventional tail rotor heli (=tricopter). The "feel" is just better.
You make some very good points.
Properly set up with a fast servo, a tricopter can certainly yaw faster than a quadcopter.
However, we have seen few if any tricopters actually competing in FPV racing.
This means either, a. people have simply not tried them or b. they don't work as well as quadcopters.
I can concede, that due to the fact that tricopters are much less common than quadcopters that not much experimentation has been done with them in FPV racing and that as a result competition tricopters have not been as highly developed as quadcopters.
But, I also think that contrary to the conclusions reached in your post, that there are also significant reasons why quadcopters might actually be superior in general.
For Quadcopters, you have already pointed out simplicity, but there is also symmetry which makes all controls intrinsically balanced.
Also although pitch and roll speed are very important, yaw speed is perhaps not so much so in general in flight and also in racing maneuvers.
As far as dynamic control, the IMU acts as a reference to which the frame continually adjusts itself according to the inputs provided by the pilot, so is intrinsically self adjusting for both quadcopter and tricopter.
There is no intrinsic imbalance as suggested, because, in fact both types achieve balance and control through dynamic fly by wire (and gyro) control.
I would also suggest that possibly the intrinsic mechanical asymmetry, mass offset and mechanical complexity in a tricopter might make it more difficult to achieve high performance.
If you make a quadcopter using an H design (especially using carbon fiber tube arms), it is possible to easily tilt all 4 motors in a desired forward direction so that rapid forward flight may be achieved with the frame level, from a practical standpoint the flight controllers IMU can simply be aligned with the horizontal axis of the propellers, so the copter will take off and hover tilted, but achieve level at some predetermined rate of speed.
All this aside, you make some very good points and I would very much like to see 2 equivalent high performance copters, one a quad and the other a tri and see what the comparative results were.