Why future racing copters really should look different.
by Dr. William Thielicke aka Willa aka Shrediquette
ABSTRACT
In this article I try to demonstrate why FPV racing multirotors need to look different. Some small modifications to the frame would (in theory…!) result in 70 % higher top speed! All that needs to be done is to align the arms parallel to the propeller flow, and to tilt the main body of the copter by about 40 degrees. I am presenting a very simple and robust racing copter design that incorporates these ideas. Furthermore, I am calculating the aerodynamic drag of different copter concepts using basic equations. The aim of this article is to make you realize the importance of aerodynamics and to stimulate people to design more innovative racing frames.
INTRODUCTION
Until recently, multirotors were mainly used as a “hovering device” and the top speed of these copters did hardly matter. Now, multirotor racing has become popular and all competitors are seeking for very fast and agile multirotors.
Apparently, the aerodynamics of multirotors have been neglected in the past (with a very few exceptions), but aerodynamics actually become very important at increasing flight velocities. Just as a quick example with numbers that are realistic for copter racing: A quadrotor that weighs 0.7 kg and flies at a pitch angle (alpha) of 45 degrees has an aerodynamic drag that is also 0.7 kg (about 7 N) – which is clearly very significant. A large portion of the force that is generated by the motors is therefore just “wasted”! If this drag could be somehow reduced, then a racing copter could fly a lot faster (or it could fly longer at the same speed).
AERODYNAMICS OF A RACING COPTER
The real flow of the air around a full multirotor has not yet been measured to the best of my knowledge. But it is very likely, that the flow around the multirotor can be divided into two distinct parts: The flow around the arms, and the flow around the main body: Directly under the propellers, the flow is pretty fast (between 100 and 200 km/h in racing copters) and it is pretty much perpendicular to the propeller disks. Just as in this picture showing the flow of a large propeller:
Usually, the flow is perpendicular to the propeller disk. The faster a propeller turns in relation to the flight speed ("advance ratio"), the more constant is the angle of the flow. |
The flow that is hitting the main body or frame is mostly horizontal, as it is hardly influenced by the propellers: It is mainly exposed to the flow velocity that results from forward flight (I however really need to verify these assumptions in a windtunnel or with in-flight measurements, I'll do that asap and report the results here).
HOW TO ENHANCE AERODYNAMICS?
It would make a lot of sense to reduce the drag of the arms below the propellers, and to reduce the drag of the main body of the racing copter. My first and simple idea to achieve this was to tilt the motors forward, and to design an aerodynamic canopy. These ideas were implemented in the “Shrediquette Gemini” in 2013 (which was later produced by Team-Blacksheep).
Some force measurements in a wind tunnel revealed that these two features reduced the drag of the copter by 14 – 40% (depending on the pitch angle).
My next idea was to tilt the body instead of the propellers. The goal was to align the body with the oncoming, horizontal flow, which will significantly reduce the aerodynamic drag. If the arms are aligned parallel to the propeller flow (= perpendicular to the propeller disk), the drag will be further minimized. My HEXO+ design (which was used in a Kickstarter project too) realized the idea of a tilted body.
The tilted body concept was subsequently ported to my next frame, the “Shrediquette QRC5” FPV racing copter:
Recently, I realized that a frame like the QRC5 is not crashproof enough for everyday FPV racing. Therefore I recently finished a “classical” FPV racing copter design that incorporates the idea of a tilted body and arms that are aligned parallel to the propeller flow. The “Shrediquette DERBE” is probably as crashproof and light as conventional racing copters, but it has much less aerodynamic drag.
The following image nicely illustrates the two main sources of drag as introduced earlier, and how drag is minimized in the Shrediquette QRC5 and the Shrediquette DERBE. The idea is to minimize the frontal area of the copter at typical pitch angles (about 50 degrees in FPV racing), and to minimize the area under the propellers.
The main body of the Shrediquette DERBE is tilted by 40 degrees. |
The following image nicely illustrates the two main sources of drag as introduced earlier, and how drag is minimized in the Shrediquette QRC5 and the Shrediquette DERBE. The idea is to minimize the frontal area of the copter at typical pitch angles (about 50 degrees in FPV racing), and to minimize the area under the propellers.
Three different concepts: Comparison of frame area (green) and area of the arms under the propeller (blue). |
CALCULATING THE BENEFIT OF ENHANCED AERODYNAMICS
The aerodynamic effects and the performance of these different frame concepts can be approximated by applying some relatively basic equations. I did the calculations in Matlab (source code here) with a numerical, iterative method. I am sure there’s an analytical way to solve the equations, but rearranging these equations would take me much more time than just letting Matlab do all the work for me…
Here is how the aerodynamic drag, and the top speed of three different copters (standard, QRC5, DERBE, each with the same motors, propellers and weight) are calculated. The numbers that I am using a suitable for MN1806 2300kV motors with 4S and 5x4” propellers:
The most difficult part of the calculations is to approximate the thrust that is produced by the motors. Thrust decreases linearly with flight speed (if the rotational speed of the motors would be constant) until it goes down to zero at some flight speed. Thrust at different flight speeds is not so easy to measure, therefore I am using an equation that seems to fit experimental data from a wind tunnel reasonably well. I am however planning to do real windtunnel measurements of the propeller performance in forward flight very soon.
Furthermore, I am assuming the flow to be perpendicular to the propeller disk below the propellers. The main body of the copter experiences flow that is purely horizontal in this simplified calculation.
The copter is set to a pitch angle (alpha) of 1 degree and full power is applied to the motors. The horizontal drag of the main body is calculated from the dorsal and frontal area of the main body at alpha, together with a drag coefficient of 1 (which is a reasonable approximation for a classical racing copter frame) and a horizontal velocity.
Additionally, the drag of the arms needs to be calculated and subtracted from the available total thrust: The flow velocity in the jet of the propeller is (based on the equations already mentioned above) approximated to be about 150 km/h and independent of the flight speed. A drag coefficient of 1.5 is assumed. To give a number already: The drag that is created by the arms of the “standard racing copter” at full throttle is 6 Newtons (about 0.6 kg)! This is equal to the static thrust of one motor…!
With the remaining thrust, I am calculating the horizontal and the vertical force component at the current pitch angle of 1 degree.
Now, the horizontal velocity is increased step by step until the drag equals the horizontal force component. If this is the case, then the pitch angle is increased by one degree and the calculation starts from the beginning. At each increase of the pitch angle, I am checking whether the vertical force component is larger than the weight of the copter (as a side note: I am completely ignoring the vertical velocity of the copter as I am only interested in the final solution where drag equals horizontal force AND weight equals vertical force).
At a certain pitch angle, the vertical force is not larger than the weight anymore. At this point, the calculation stops and both the pitch angle and the velocity of the copter are printed.
Here are the results:
Standard racer | Shrediquette QRC5 | Shrediquette DERBE | |
Max. tilt angle [deg] | 38 | 29 | 34 |
Top speed [km/h] | 107 | 178 | 170 |
The numbers for the “standard racer” seem pretty realistic, although I am quite sure that the top speed is always overestimated. It is very likely that there are additional sources for drag on a copter that were ignored in my simplified assumptions, and that the hypotheses on thrust vs. flight speed could be improved. However, I am doing the same errors in the calculations of all three copters, therefore the above results represent the correct trend: Aerodynamic designs fly much faster and at lower pitch angles. These two factors a highly relevant in FV multirotor racing and in the future, more attention should be paid to designing simple aerodynamic copters like the Shrediquette DERBE. Furthermore, I will be experimenting with optional airbrakes in the first prototype. These will be deployed at very low throttle and when the throttle is quickly reduced (hence reacting to the derivative of throttle). In my imagination, this could really help on tight racetracks, as it enables the pilot to brake without having to change the pitch angle (which would take more time and also results in a camera that points to the sky).
A few renderings of the Shrediquette DERBE (more soon):
I just received all parts and really quickly snapped the parts together. Everything seems to fit really well :-D
Nice Article!
ReplyDeleteI also wonder if or better HOW the different angles showup on a racetrack - unfort. I also think about different angles for front and rear motors and how this affects the flyability...
Hard to explain by words but if you have more angle on the rear and a flatter fron angle the rearmotors should more push and due to the punch the front motors more responsible to let the racer keep on level...
Or as I also saw in Bexbach the try to have a more bended angle to the outside as acro quads...
It's hard to say whats better... For just fly straight maybe but on a track where you can't suffer from long straight trackparts you might loose much punch in the turns...
But I like that someone starts over and trys to calc the behaviour!
thx!
What's the weight of the DERBE?
ReplyDeleteHi, I don't know yet... But the laser sintered parts do not really add weight, they're light and super robust.
DeleteQuick question: Vpitch for a 4" pitch prop is around 220km/h (2300kv*16V*4"); isn't Vmaxhorizontal at a 34 degree pitch of the copter sin(34)*220=125km/h? Or is that approach too simple? that is even without any drag. just wondering how your results are showing 170km/h for the Derbe....
ReplyDelete170 km/h surely is an overestimation as I also mentioned in the text.
DeleteYour approach to calculate the speed is not correct as far as I know. You can calculate forces in this way but I don't think you can do that with velocities... But I am traveling right now and can't think about this in more detail...
David Windeståls Minitricopter has been GPS logged doing 169 km/h so Im not sure it is an overestimation William :) THe MiniTri also has very little front area
DeleteBR/ Kajaken
Of course you can do that with speeds, that's how navigation of planes and ships works.
DeleteAnyway, totally missed you mention that.
DeleteDr-
ReplyDeleteI have been thinking about this for some time and I have 2 points/questions to pose:
1) given that most racing quads have about 2.5:1 lift to weight ratio, then flying at 45deg seems inefficient. If you apply full throttle, you would climb too much if you were only pitched 45deg.
It would seem that, to maximize the available power, you would have to fly at an angle of attack that is 2.5:1 off of vertical. This is more like 75deg (maximum). Does this sound right?
2) The airflow coming from the props is helical. while you gain much efficiency by using your vertically oriented arms, do you waste some of the energy when those arms "divert" some of the propeller wash? would it be better to place the arms above the props to allow the flow off the propellers to flow as uninterrupted as possible?
2: yes that would very slightly increase the thrust, because the flow is faster below the prop (because it contracts).
Delete1: If you know the thrust at the specific speed you're flying at , then you can calculate what pitch angle would be best. But thrust decreases with speed, that makes everything a bit more complicated...
I had also thought that another consideration is the resonant frequency of the arm material since vibrations are most pronounced on the plane of the propeller. I'm not an engineer so I do not know the correct terminology but vibration in this plane would tend to flex the arm in its weakest direction. has this issue presented itself?
DeleteI designed a concept like this but I turned all of the electronics (naze32, etc) in their sides. Of course, the battery still presented a large face to the airflow.
First, awesome work. I can appreciate the time it must take to work on this as a hobby plus handling everything else!
ReplyDeleteMaybe slightly off topic but have you ever considered developing you frame with a material similar to the HMB-235? I mean you do intend to have the thing going 100km/h + so would it not be cool if you could take a good hit and not worry too much? Not sure if you have seen that frame in action but its crazy durable! Hope you don't mind I link it here. Plain quad design but with your skills you could shape that material into something beautiful!
http://www.multirc.com/products/27/HMB-235
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