To Tricopter or to Quadcopter ..... That is the Question


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.

equation #1:

Thrust(M1) + Thrust(M2) + Thrust(M3) + Thrust(M4) = Total Thrust  ... and this is determined by Thrust Stick only.

equation #2:
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:

equation #3:
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:


equation #1:
Thrust(M1) + Thrust(M2) + Thrust(M3) = Total Thrust ... and this is determined by Thrust Stick only. same as quadcopter.

equation #2:
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:

equation #3:
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.

Views: 4642

Comment by MHefny on October 27, 2015 at 12:11am

Gray

I liked the idea of tilting the board, either physically or in firmware.

Leonard,

Thanks alot man.... alot of info here I didnt know.

What I try to suggest here is that tilted Tricopter with adapted firmware to Keep the frame horizontal whatever condition will allow it to go fast because you can then build an aerodynamic body that will face wind from front only. as the tilted Tri is capable of speed up by change front motor tilt rather than tilt forward the body.

Could u guys give me feedback on this point.

Comment by Andrew Zaborowski on October 27, 2015 at 3:08am

Gary,

I haven't used digital servos yet.  In my experience the servo's power draw is minimal.  The reason I mentioned micro quads is that you generally have smaller batteries on them, and there, and additional 100mAh might be an issue.  At anything bigger you won't even notice it.

The efficiency gain I believe is also a result of having fewer motors but coming up with data to back this up would be difficult.

I do agree with Leonard on most points, except on the motor tilting.  But I also find most of the tilting motor designs a little silly, here's why.

An H quad's centerpiece tends to have a considerable surface area.  With statically mounted motors that surface is perpendicular to the air flow so it's a source of inefficiency (admittedly a small one, because most air flow is through the rotor discs).  When you're in a translational motion most airflow over the copter is still perpendicular to the rotor discs even though it might seem like you're flying a fixed wing.  In a fixed wing the airflow over the body is the opposite direction of your movement and there, keeping the body flat obviously makes sense.  In a copter what you should be doing when moving forward is to actually tilt the airframe slightly to the back while tilting your motors forward, if you care about the aerodynamic properties which I'm not sure is really worth the effort anyway.


Developer
Comment by leonardthall on October 27, 2015 at 3:49am

Hi MHefny,

If you tilt the front two motors forward you will get a good low drag profile. You will need to adjust your pid gains to ensure the roll authority doesn't drop and the copter becomes unstable. You could probably go to 60 degrees using this simple approach and get good results.

Tilted motors on quads:

There are a bunch of problems with that approach and all depend on the particular implementation. Just rotating a standard quad's motors forward quickly results in halving the disk area and killing your pitch control. The result is much lower efficiency and poor control.

A better design is to improve the aerodynamics in that fast forward flight condition. This was my first attempt and I achieved 140km/h sustained flight at 60 degrees lean angle. This could have been faster if I didn't have to carry a relatively large payload.

http://diydrones.com/profiles/blogs/printed-high-speed-avc-copter-a...

I have a plan for my next version :)


Developer
Comment by John Arne Birkeland on October 27, 2015 at 5:26am

Tricopters tend to be a favorite if the pilot has previous experience flying helicopters since the feel is similar. Another plus for tri is that it's easier to keep visual orientation. But other then that, quad wins in most areas.

Comment by Mark on October 27, 2015 at 5:38am

Hi Guys,

Our experience is mostly with designing/building/selling racing quads although we are developing a mini tri at present because they are cool and fun!

Thought I would make some observations:

a) the popularity of mini tri frames has fallen in last 18mths.  IMO, this reflects the improvement in yaw performance of the FCs last year. Before that, it was just hopeless on mini quads. Some of you will remember V tails....

b) quad high speed turns are completed with min of yaw. Mostly roll and throttle to compensate.

c) Power to weight ratio is an important consideration for a race quad.  Our latest quads are in the 8+ range and we will test a new design concept next week with power to weight ratio of 11+ .  You cant easily do this with three motors!  We hope to try and crack 150km/hr on 4S with 6in blades. Not sure if we will get there but are getting close already with 5in props.

d) high speed digital cyclic servos make a big difference to our tri's. On our mini 250 size tris, we use digital coreless 3kg 0.07s servos. Cost penalty is 20grams.  Power draw, who cares, just make the thing go faster :)

e) Well designed lightweight cnc alu mechanisms are not widely available. Major negative based on my discussions with our customers. 

On a side note if I can digress, quads (tris) have poor aerodynamics (except, love leonards 3d printed racer). What more can you expect with big slabs fighting the apparent wind with all of the newtons pushing you downwards. The very latest designs are a lot better (BOLT210, Krieger etc). eg. we achieve 20-30km/hr increase in speed just through better designs compared to BOs and QAV style frames.  

We dont use motor tilts. Our race quads fly at ~70 degrees at speed. We believe that 45 degrees is the worst angle for a quad. Once you are past 45degrees, the increased resistance is offset by the reduced down force. If we were flying an old style H quad, I presume the opposite would be true, ie. every degree below 45 would be an advantage, hence the benefits of motor tilts. I plan to run some cfd sims in coming weeks to test this theory further.

Hope I did not digress to much from your tri analysis.

Cheers

Mark

Comment by Gary McCray on October 27, 2015 at 6:24pm

Just to clarify I wasn't talking about active motor tilting.

There actually are a few quads that have active motor tilting, but I don't think the gains are worth the extra mechanical complexity and weight, although at least one example does achieve very high speed forward flight.

I was suggesting fixed equal forward tilt on all 4 of a quads motors to allow alignment of the frame with the direction of travel and this definitely benefits more if a lightweight aerodynamic shell is included.

According to mark, a severe tilt might be a real advantage for racing, but it is possible that a shell that was aerodynamically neutral at the at speed achieved tilt would work too.

Since it also presumes optimal operation at a specific forward speed, this design is really only optimized for high speed or competition FPV use.

Probably not so useful for general purpose or video or photo use although if you were doing follow me on action sports - maybe.

Actually a bigger problem that I continually see is the use of flat wide motor arms that interfere excessively with the propeller downwash.

This is because it is easy to make CNC G10 or carbon fiber arms even one piece with the main frame.

It does not provide optimal prop efficiency however and is solid flat plate area, so a dead loss to propulsion.

Round tubes cut the loss in half and aerodynamic arms can make it vanishingly small, basically the horizontal flat arms are awful.

Just basic aerodynamics 101.

You can also mount the motors under the arms because in-wash losses are much less than output losses.

But then you have problems with ground clearance and landing gear.

This stuff holds true for both quads and tris, but tilting the movable motor forward is not so easy on a tri.

Best,

Gary

Comment by John Rambo on October 28, 2015 at 2:33am

So personal observations:

- In bright daylight TRIs give much better orientation feel (completely Agree to Jonh)

- If servo is not undersized (thus increasing its realiability), less ESC/Motor count results in higher reliability for TRIs

- More space on the frame, the space which isn't covered by Props

- On SERVOs:

- In my tests micro servo has never exceeded 2Amps @ 5Volts.

- If you stall a servo, however, that will virtually kill 5V RAIL, resetting Flight controller etc. So limiting servo motion boundaries via configuration, but not mechanically is crucial.

- A separate 5V RAIL is recommend for a servo.

- Stock (i.e. HK frames) servo mechanisms are absolutely impractical - torque direction rods are tilted (thus reducing effectiveness), to many parts which break upon every stronger impact. Bolts get loose upon each flight. Simple, well built tail boom can eliminate most of problems with TRIs.

Comment by Mark on October 28, 2015 at 6:40am

Hi Gary, 

Apologies, I missed the point re non mechanical mech tilt.

BTW, the aerodynamics of arms are less of an issue with the newer quads as the arms are around 14mm wide but thicker.  They would be even less but for the escs being around 13mm wide. Despite the thin arms, better engineering sees these quads nearly as strong as the usual paddle pop arms.

To clarify, I dont believe (untested as yet) forward motor tilts are a positive unless the quad flies in the ~45 degree range.  In fact, we plan to test reverse tilts shortly to increase the angle the quad flies. 

Cheers

Mark

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