I´ve did a small numerical exercise in order to improve the flight time for an electrical quadropter.
I did for a family of 5 quadropter weights from 500g to 1.5Kg, dry mass, (without battery).
The hipothesis are the following:
- power consumption is linear with total weight: Watts = 0.15 * weigth(gr). The ratio is taken from tests on my quad (730gr , 110 wat)
- battery weigths taken from Zippy & Turnigy Lipoly 3S 20C data at HK (average wights for a standard model) It can be expressed as: Batt Weight (gr) = 0.0688*Capacity(mAh)+26.5 )
The result is the following table:
For example a quad of about 500gr (dry) with a battery of 2200mA is very good compromise, reaching about 15min flight time. In fact, one of my quadropters about these data, reached 17.5min continous hovering flight with a battery of 2250mA.
Attached is the excel file, if someone wanst to play more.
Hope you like
Note. This is an update of initial issue with better data (averaged) from comertial battery weights
Very interesting especially that 'flat' spot.
Hi. For what I can understand from the graph and table, even if the 500gr is a good compromise, it looks like the heavier it gets, more efficient it gets too. The 1500gr model with 4400 battery does not consume 3x the power of the 500gr model, and the flight time is more than 1/3 of the 500gr time. Is that correct ?
Sorry: updated graph with averaged battery weights made dissapear that flat spot. But you can get it againg paying more money for lighter batteries, same capacity. For example, for 2200mAh you can get a wide range of weights depending in max I and model (I´ve used 20C) : from 135gr to 190gr.
What happens is the heavier it is the copter, the battery weight less impact has. See figure below. On a 500gr quad, a 3000mA battery is the 35% of the total weigth, but in a 1500gr quad is only a 12%.
The problem of electrical source (battery) compared with fuel is that in electrical you always keep all the weight along with the flight. In fuel, the fuel weigth decreases with the time. And this effect could be very significant, mainly for smaller machines, where the battery weight % is important (like in the example before).
But this is inherent to the flight time duration: the longer is the flight time (electrical), the longer is the time you flight a "dead" mass. For electrical flight the best solution could be to flight, let say 3 batts using one after the other and let drops each one once is empty (the same that space rocket launchers does using several stages).
But if your parameter is to fly longer without changing batteries, you should choose as light quadropter as possible.
The most critical factor in rotor hovering efficiency is disk loading. There is also a figure of merit to consider here, which is the aerodynamic efficiency of the propeller itself. These model airplane propellers were typically designed for low Reynolds numbers and high advance ratios (forward speed versus blade pitch). Static (hovering with no forward movement) thrust is often very hard to predict, but all things being equal, the less weight you try to lift with more effective rotor disk area, the better off you are. Lifting force is basically the mass of air times the acceleration, but because the power required will increase with the cube of the inflow velocity, it's much better to take in a large volume of air and accelerate it a little (i.e. get larger diameter props and reduce the RPMs). If you wish to learn more, I highly recommend Dr. Gordon Leishman's book Principles of Helicopter Aerodynamics, especially chapter two where the fundamentals are covered.
Great Info. Thanks!
Also, in a quadrotor with stabilized control, the way this work is done affects a lot to the consum, and so the flight duration. Large props, being the best for aerodinamic effitiency, has biger mass and inertia and the control corrections paid more consum than lighter props. I´ve compare (like many of you, sure) different prop sizes in same copter, and there is an optimum for each specific coper (size and mass) and control code strategy.
In general, the lighter is copter, the smaller are the optimum props (needed also for coherence with the smaller motors capacity).
In my case, I´ve tested that:
Copter mass=650 gr > optimum prop = 8x4
Copter mass=1000 gr > optimum prop = 10x4.5
Comparing times in a 650g copter: with 8x4 props I reach 17.5 min (2.2A batt) and only 15min with 10x4.5 props.
Really nice work.
...and what about Quad vs. Hexa ? ;-)
I can see that rotational inertia plays a huge part in the control responsiveness of the copter, but I think you're rather seeing the aerodynamic differences at work too. Larger disk area for a given weight is still better, all things being equal, but all things are rarely equal.
Model airplane propellers are really not designed for static thrust, which is a whole different operation condition than forward flight in a fixed-wing aircraft. I have tested a great many different propellers and rotors, both commercially available and custom made, in my admittedly crude testing stand. In short, I can tell you from experience that multicopter flight times could be easily DOUBLED if someone would design a series of propellers for this community that were specific to our application. Of particular interest are three things: proper airfoil selection for each radius station, planform taper (chord getting smaller toward the tip), and most importantly, pitch. The visual differences in airfoil cross-section shapes can be subtle, but the performance differences, huge. Note that in the Martin Hepperle series of airfoils for example, I've found the MH-114 to be wonderful but the very next one in the line - the MH-116, to be practically useless when an entire blade is made from one airfoil. His JavaProp program is a wonderful simulation tool, by the way, and certainly worth a look: http://www.mh-aerotools.de/airfoils/index.htm
If you can have a consistent series of programmed maneuvers for your testing to form a solid baseline for comparison of "maneuvering efficiency", I strongly recommend trying different manufacturers propellers, paying close attention to not only size but blade pitch as well. Blades are all numbered for diameter and advance ratio, and you'll need to covert this to degrees of pitch to understand what you're testing. Solve for the angle by trig; an 8" propeller has a 25.13" circumference and a rise of 4, for a rated pitch angle of 9.04 degrees (provided the maker rated it properly-some don't). The 10X4.5 has an 8.16 degree pitch. Yes, one degree can make a difference, but I suspect the differences between the two props you tested are more than just mass and one degree of pitch.
Thank you for your efforts. Certainly much more work needs to be done in this area for the small multicopter community.
I´ve never fly Hexa. But I´ve tried Tricopter and bicopter and, I can say that the less number of motors you have, the best global effitienty (longer flight times).
For example a Tricopter is more effitient than a cuadropter globally. But tricopter has complex mechanisms (the tail balancing motor).Stability and maneoubrability is not so good as the quadropter.
A bicopter is even better, but this is really in the limit of stability (not usefull).
Cuadropter is a very good compromise:
So we can conclude, quadropter is the best selection for standard performances. Maybe HEXA are better for some specific requirement, but I don´t know.
The two primary benefits of hexa/octo I have observed in my calculations, and have heard discussed are:
* heavier lift capacity
allows you to maintain "most efficient" lift range with similar motor/props, where otherwise you need to upgrade to less optimal or nonexistent motor/prop, or run the RPMs up outside of the best performance for existing propulsion system)
potential for controlled flight after the loss of esc or motor
The former (weight) is very directly related to the characteristic most often thought about last by the novice engineer, target weight, something in a MAV that I suspect should be considered first, or returned to cyclically in the design cycle as the most significant input. But that is the opinion of a novice ;)
I would have tought that a hexa is way more better than a quad or tri.
I thought the more motors share the weight, the less power consumption there is. Especially if I try to speed up and break..more motors can handle it more effective.
Did I make a mistake in my thoughts?