Comparing cubic wing load and power loading.

[Tench745]

I have this train of thought I am currently following and I thought maybe some others might want to weigh in on it. It's a theoretical and number crunching problem.

As many know, wing loading is a terrible way to compare how aircraft of different sizes will fly. To compare models of different size we use cubic wing loading, which gives us a number we can compare pretty universally across all sizes of aircraft. They fall somewhere in the following categories:
Slow-flyers and Gliders: under 4
Trainers and Parkflyers: 5 to 7
Aerobatics: 7 to 10
Scale: 10 to 15
Warbirds and Racers: 15 and over

When sizing motors we have compare watts/pound depending on the type of flying you want to do. The categories are something like the following, depending on who you ask:
50 -70W/lb. …....Trainers and slow flyers
70-100 W/lb. .....Basic aero/sport flying
125 W/lb. …........Precision aerobatics
150+ W/lb. …...…Extreme 3D performance

My current line of thinking is: why do we compare power to weight directly? Would there be any benefit to comparing power to cubic wing load?
I crunched a few numbers to start a comparison. All data for the given aircraft are from Wikipedia based on rated power and maximum weights, so they don't necessarily reflect actual use cases of a given aircraft.

- A full scale Cessna 172R has about 160hp(119312W) and a gross weight of 2450lbs, for a power to weight of ~49W/lb. At gross weight a 172R would have a cubing wing loading(WCL) of 17.1.
- A Zivko Edge 540 has 310hp(231167W)and a max aerobatic weight of 1550lbs, for a power to weight of 149 W/lb. At its aerobatic weight the Zivko Edge 540 has a WCL of 22.7.
- A J-3 Cub has 65hp (48470.5W) and a max weight if 1220lbs for a power to weight of 39.7W/lb. Its WCL at max gross is 8.2.

 

[JasonK]

Power to weight would show some sort of acceleration capability. (it is also an approximation as you could have a low pitch prop that gives you plenty of static thrust, but a low top speed or a high pitch prop that gives you a high top speed, but low static thrust(

IE to do anything 'fancy' with flying you need plenty of thrust compared to weight. (and it is really weight to thrust/power that says if you can power out of a stall, have enough power to pull a loop/acrobatic maneuvers. 3D is going to require more thrust then weight as you need to hover on the prop, not just fly on the wing)

those real planes aren't ask to power out of stall, do loops, or any other acrobatic maneuvers. (I would expect them to also have better airfoils and better lift to drag ratios then our hobby stuff, they also tend to have variable pitch props and other optimizations - therefore they can cruse with less power to weight ratio then it takes to do acrobatics with our toys).

WCL has to do with the relative speed needed to have enough lift to fly (lower WCL, the lower scale speed needed to stay airborne), which is a bit different of a measurement.

 

[Piotrsko]

Just so you know: me and my slope gliders kinda destroy your last statements.

"Ve don need no ztinkink motors". The only thing I couldn't do was a square loop, but only because I kept breaking the plane at the first pull up but on a good day, it would hover. The slab sided ones would do knife edge but it was hard with only yank&bank.

 

[SSgt Duramax]

I think things like aspect ratio, chord, and airfoil shape come into play alot too. I think even looking at these two things together is very limiting.

First off, I have no clue how many watts my motor makes, and I'm not even sure how relevant that is to me. Much like cars, this can come in different power deliveries, and every motor/prop set up should act different.

For instance, if I were to take one of the F Pack motors that I love so much that makes around 350W with a 6045 prop that I love to use, and put it on a 2 pound plane to be used for 3D. It would easily meet the 150w/lb requirement, yet it would fly like complete garbage, and we all know it would fly like complete garbage, but may not be able to tell you why right away.

I think coefficient of drag/aerodynamic cross section to prop speed ratio would be probably fairly efficient for measuring how efficient and fast a plane would be.

I think the watt to pound thing is to a point good to measure acceleration, but also of course prop pitch plays a pretty big role as well.

I was a car guy before a plane guy, so I tend to put things into 2 categories, there is the "torque" category and there is the "horsepower" category. I had a 500whp Duramax, and now I have a 500whp Audi, they both make the same power, but do two very different things.

One would go only 120mph, but get to 30 very fast, haul 10000lb of concrete, and do it anywhere over any surface while using boatloads of fuel. (Low KV motor, low pitch prop, low wing loading, aerodynamics of a brick). This truck made over 1000lb/ft of torque.

My other one will go 180mph (I still have yet to confirm this, but I will at the Texas mile) rip past 100mph in no time on the speed gauge, but it takes a second to get spun up and doesn't tow that much, but nets me about 30mph if I keep it under 80mph on the interstate. (High KV motor, High pitch prop, higher wing loading, very slippery aerodynamics). This car makes less than 400lb/ft of torque.

 

[JasonK]

Just so you know: me and my slope gliders kinda destroy your last statements.

"Ve don need no ztinkink motors". The only thing I couldn't do was a square loop, but only because I kept breaking the plane at the first pull up but on a good day, it would hover. The slab sided ones would do knife edge but it was hard with only yank&bank.

your 'motor' when slope gliding is that up draft.... compared to the air, your 'diving' much/most of the time. yes you could do that same thing with a motored plane (dive to get the speed you need to perform a maneuver). Wouldn't "hovering" a slope glider just means your sink rate matches the up draft speed (which is different then hanging on power).

 

[SSgt Duramax]

your 'motor' when slope gliding is that up draft.... compared to the air, your 'diving' much/most of the time. yes you could do that same thing with a motored plane (dive to get the speed you need to perform a maneuver). Wouldn't "hovering" a slope glider just means your sink rate matches the up draft speed (which is different then hanging on power).

I get what he is saying, that your "standard rules of thumb can be hogwash" kind of the comparison I made on the 350w 2207 motor on a 3D plane weighing 2 lb. It would be less than spectacular and wouldn't perform well at all but it "follows the rule"

I think in a sense, what everyone is kind of getting at, is there some sort of metric that we could get to that would be a little more fool proof? If could accurately measure the drag coefficient of a plane, accurately calculate lift of a wing and the drag (lift to drag ratio) and know when thrust is your important measurement or pitch speed is the one to optimize for, then that will get you closer to what you want.

 

[Tench745]

those real planes aren't ask to power out of stall, do loops, or any other acrobatic maneuvers. (I would expect them to also have better airfoils and better lift to drag ratios then our hobby stuff, they also tend to have variable pitch props and other optimizations - therefore they can cruse with less power to weight ratio then it takes to do acrobatics with our toys).

Some points worth noting about the full-scale examples:

I threw the Edge 540 in there to give an example that was quite different from the other two planes. It is a fully aerobatic aircraft and is quite capable of most any aerobatic maneuver you might want it to perform.

The J-3 and the Cessna 172 both have fixed-pitch propellers, whereas the Edge 540 has a constant-speed prop.

Variable pitch props don't necessarily let you cruise with less power. they allow you to operate more efficiently across the whole speed range. With a fixed pitch prop you have to choose which end of the speed range you're optimizing for. So, you could put on a prop that is great in cruise, but lacks the oomph for good climbs or you could put on a climb prop that will be less efficient in cruise, or split the difference somewhere in the middle. The same applies to our models. For an automotive comparison, a variable pitch prop is like a transmission and a fixed pitch prop is like a mini-bike or go-cart where you have to pick one gearing that will meet your needs.

First off, I have no clue how many watts my motor makes, and I'm not even sure how relevant that is to me. Much like cars, this can come in different power deliveries, and every motor/prop set up should act different.

For instance, if I were to take one of the F Pack motors that I love so much that makes around 350W with a 6045 prop that I love to use, and put it on a 2 pound plane to be used for 3D. It would easily meet the 150w/lb requirement, yet it would fly like complete garbage, and we all know it would fly like complete garbage, but may not be able to tell you why right away.

The power-to-weight ratio rule of thumb assumes you will apply that power in an appropriate manner, sizing the motor kv, gear ratio, and prop for the needs of the model.
I would argue that if you added a reduction drive to that F-pack motor so it could swing a larger prop at lower RPM it very well may haul a 2-pound plane around without issue. In the same way that a 500whp Duramax with the right transmission could probably make that Audi just as fast. Obviously there is a reason Audi didn't go that route because the vehicle as a whole is a package designed to work together.

I think coefficient of drag/aerodynamic cross section to prop speed ratio would be probably fairly efficient for measuring how efficient and fast a plane would be.

I think the watt to pound thing is to a point good to measure acceleration, but also of course prop pitch plays a pretty big role as well.

If you under prop motor it will take less power to spin, so your watts/pound suffers accordingly.

I think things like aspect ratio, chord, and airfoil shape come into play a lot too. I think even looking at these two things together is very limiting.

I agree entirely that there is more to the equation than just these two metrics. None of these data points by themselves tell the whole story and they all affect one another. I have a book which discusses the mathematics of model airplane design; how to use drag coefficients and Reynolds numbers and all that to really nail down a model's potential performance. I was mostly looking at the relationship of wing loading, cubic wing loading, and power-to-weight ratio and how they relate to one another when scaled.
I was focusing on these few metrics because they can give you a quick, back of the napkin look at how a given model may perform and I was curious if relating them to one another might show a correlation between the low wing loading gliders that can fly at 30W/lb and the heavy warbirds that might need 200+W/lb to perform. I believe in the full scale world they sometimes reference "power loading" which is the ratio of horsepower to wing loading. But, scaling this down probably has little use to us modelers because of how wing loading scales.

 

[SSgt Duramax]

Some points worth noting about the full-scale examples:

I threw the Edge 540 in there to give an example that was quite different from the other two planes. It is a fully aerobatic aircraft and is quite capable of most any aerobatic maneuver you might want it to perform.

The J-3 and the Cessna 172 both have fixed-pitch propellers, whereas the Edge 540 has a constant-speed prop.

Variable pitch props don't necessarily let you cruise with less power. they allow you to operate more efficiently across the whole speed range. With a fixed pitch prop you have to choose which end of the speed range you're optimizing for. So, you could put on a prop that is great in cruise, but lacks the oomph for good climbs or you could put on a climb prop that will be less efficient in cruise, or split the difference somewhere in the middle. The same applies to our models. For an automotive comparison, a variable pitch prop is like a transmission and a fixed pitch prop is like a mini-bike or go-cart where you have to pick one gearing that will meet your needs.



The power-to-weight ratio rule of thumb assumes you will apply that power in an appropriate manner, sizing the motor kv, gear ratio, and prop for the needs of the model.
I would argue that if you added a reduction drive to that F-pack motor so it could swing a larger prop at lower RPM it very well may haul a 2-pound plane around without issue. In the same way that a 500whp Duramax with the right transmission could probably make that Audi just as fast. Obviously there is a reason Audi didn't go that route because the vehicle as a whole is a package designed to work together.



If you under prop motor it will take less power to spin, so your watts/pound suffers accordingly.


I agree entirely that there is more to the equation than just these two metrics. None of these data points by themselves tell the whole story and they all affect one another. I have a book which discusses the mathematics of model airplane design; how to use drag coefficients and Reynolds numbers and all that to really nail down a model's potential performance. I was mostly looking at the relationship of wing loading, cubic wing loading, and power-to-weight ratio and how they relate to one another when scaled.
I was focusing on these few metrics because they can give you a quick, back of the napkin look at how a given model may perform and I was curious if relating them to one another might show a correlation between the low wing loading gliders that can fly at 30W/lb and the heavy warbirds that might need 200+W/lb to perform. I believe in the full scale world they sometimes reference "power loading" which is the ratio of horsepower to wing loading. But, scaling this down probably has little use to us modelers because of how wing loading scales.

Yeah, it is best to figure out what you want to do with a plane, and figure it out what things you want to optimize. Your typical flite test design is fairly easy to fly because it has inefficiencies in other places.

The transmission in that analogy is the pitch speed. The car transmission is great of efficiency and speed, and the truck transmission is good for stump pulling and such. Horsepower and watts are the same thing, but they can do two different things depending on how they are delivered, packaged, and utilized. Be it gear ratio or propeller pitch, or whatever. I realize that two 500hp engines given gearing to achieve the same speed in every gear would in theory accelerate the same and deliver the same efficiency, but they don't. There is a reason that the 450hp semi truck engines aren't high strung turbo 4's or even a 6.2L small block chevy, but 15 liter inline 6's.

 

[Scotto]

This is an interesting conversation. I love how incredibly different planes can look from each other and still perform similarly, but every plane has to be balanced just right for its configuration.
I was just thinking when a 3d plane is hovering on the prop, the prop is the "W" in the WCL like a heli, right? So how do you calculate a heli and should the speed of the rotor or fixed wing in our case have to be in the equation?
The equation might have to be plotted on a graph. Maybe you could approximate the speed envelope from there? Maybe not. The airfoil would matter so much.

 

[Tench745]

I was just thinking when a 3d plane is hovering on the prop, the prop is the "W" in the WCL like a heli, right? So how do you calculate a heli and should the speed of the rotor or fixed wing in our case have to be in the equation?

As I understand it, as the plane pitches up the wing essentially stops generating lift and you begin to fly on the prop. It would probably be more accurate to say that the vertical lift component of the wing decreases. As this happens the plane begins to rely on the thrust of the prop to hold it in the air like a helicopter, as you said. If you want to do 3D stuff where you can fly on the prop and not the wing you will want to size your power system for higher thrust numbers (typically a lower kv motor swinging a large diameter, low pitch prop). If you want to hover you will want a static thrust number equal to or a little more than your flying weight. If you want to do vertical climbs you will need more static thrust than the model's weight.
Watts, or more generally power, is measuring a force applied over a distance in a given time.
If you increase the force applied, increase the distance it's applied over, or reduce the time taken to cover that distance you are using more power. So for our vertical climb example, if you have a plane that can climb( lift its weight) one foot in one second it takes a certain wattage to achieve that. If you double the wattage (and size the motor/prop accordingly) now it could climb two feet in one second.

I lost my train of thought and I think I'm just rambling now... for someone who struggled with physics in high school, I find the math of all this quite fascinating.

 

[Scotto]

Sorry if I derailed your train of thought. I guess a more accurate formula would have drag in there somewhere but thats pretty hard for us to know.
Maybe what you need is a Watt cube loading?

 

[Monte.C]

LOL you guys'll never find a formula to describe turbulence. My motto is "Shut up and build a plane."

 

[SSgt Duramax]

Sorry if I derailed your train of thought. I guess a more accurate formula would have drag in there somewhere but thats pretty hard for us to know.
Maybe what you need is a Watt cube loading?

That is kind of what I was eluding too, and kind of hard to answer. You can technically fly 3D on a giant box with control surfaces. Aerodynamics doesn't matter as much as if you are trying to get the longest flight out of a battery pack or go 100mph. It probably helps that trainers aren't terribly aerodynamic. My slippery planes pick up speed sometimes when I don't want them to! Imagine getting used to the controls and the wind hits just right and all of the sudden your plane is going 50mph!

LOL you guys'll never find a formula to describe turbulence. My motto is "Shut up and build a plane."

Yeah, when dealing with dollar a sheet foam, it is probably better just to guess and check, just the more educated guess you have, the less checking you have to do after guessing though. I don't need a formula to tell me that when my engine is spinning its guts out, and the plane is struggling to stay in the air, the plane either needs to be lighter, have a different wing set up, or a bigger motor. It isn't like we are building supersonic jets, or trying to fly 20 miles on a 1000 mah battery pack. The time/effort to do stuff like that would be insane, and only be required by less that 1% of the people on this site, who probably have most of this stuff figured out.

 

[Monte.C]

I mean if the math is what gets you off, then go for it, find your satisfaction that way.

But formulas work for sizing steel for buildings and bridges. Planes are more complicated than that. That's why we wind up relying on wind tunnel tests.

A wind tunnel is the admission that your question is much harder than you'd like it to be, so you'll have to just build a scale model and test the design under real conditions, measure the snot out of it and graph the results in the hopes that you can extrapolate off that and reach some sort of somewhat reasonable estimation of what the design might do full size. It means you can't figure this out on paper.

I can "algebra" circles around most people, but it's a whole lot easier - and for me, much more satisfying - to draw up something new, loosely based on previous experience by myself and others. That's stuff that even I can wrap my head around. I just don't care to throw math at a problem I'll never ever get a precise answer to. I suppose we each have different interests. Anyway it's good the hobby can bring us together here. Sorry I sound argumentative; I should just stay off your math thread. Peace.

 

[Scotto]

I mean if the math is what gets you off, then go for it, find your satisfaction that way.

But formulas work for sizing steel for buildings and bridges. Planes are more complicated than that. That's why we wind up relying on wind tunnel tests.

A wind tunnel is the admission that your question is much harder than you'd like it to be, so you'll have to just build a scale model and test the design under real conditions, measure the snot out of it and graph the results in the hopes that you can extrapolate off that and reach some sort of somewhat reasonable estimation of what the design might do full size. It means you can't figure this out on paper.

I can "algebra" circles around most people, but it's a whole lot easier - and for me, much more satisfying - to draw up something new, loosely based on previous experience by myself and others. That's stuff that even I can wrap my head around. I just don't care to throw math at a problem I'll never ever get a precise answer to. I suppose we each have different interests. Anyway it's good the hobby can bring us together here. Sorry I sound argumentative; I should just stay off your math thread. Peace.

Think that formula will be there and it will be there. Its a mother beautiful formula, and it will be there. Ok?

Btw you are so meticulous on the little details of your planes I have a hard time believing you wouldnt do math for 5 minutes if Tench had something to help you scale your plane to your motor.

 

[Monte.C]

View attachment 223154
Think that formula will be there and it will be there. Its a mother beautiful formula, and it will be there. Ok?

Btw you are so meticulous on the little details of your planes I have a hard time believing you wouldnt do math for 5 minutes if Tench had something to help you scale your plane to your motor.

"Mother beautiful bridge" one of the best film phrases and I can never even figure out why. Must be his character and his delivery.

"if Tench had something to help you scale your plane to your motor." Honestly I'm pretty much locked in to a certain size plane because... reasons, so I wound up with a pretty good idea what size motors and batteries work for me. But it's nothing a couple well-placed questions among friends here couldn't answer.

Anyway, math is cool. Just a little dry for my taste. I'm more for deciphering things in three dimensions. Thanks for your consideration though Scotto.

 

[SSgt Duramax]

"Mother beautiful bridge" one of the best film phrases and I can never even figure out why. Must be his character and his delivery.

"if Tench had something to help you scale your plane to your motor." Honestly I'm pretty much locked in to a certain size plane because... reasons, so I wound up with a pretty good idea what size motors and batteries work for me. But it's nothing a couple well-placed questions among friends here couldn't answer.

Anyway, math is cool. Just a little dry for my taste. I'm more for deciphering things in three dimensions. Thanks for your consideration though Scotto.

I know good math.... add F pack motors until it flies. If it is below a yard wing span and decently under 2lb, and F pack motor will probably pull it. 2 of them make my 3lb UAV fly straight up.

Around or over 2 pound plane? a 3536 works great. You can make those lift big heavy things or go 50-70mph.

If you want a slow flyer that is somewhere in the middle, there is B and C packs, but honestly, I am at the point if it calls for a C pack, just go ahead and toss a 3536 on it. I picked up a couple more for 15 bucks each. I have no need for my C pack motors anymore. I think I'll sell them, but I do want to build that skymaster. Might keep a couple around for that.

 

[Piotrsko]

Watts, or more generally power, is measuring a force applied over a distance in a given time.
So for our vertical climb example, if you have a plane that can climb( lift its weight) one foot in one second it takes a certain wattage to achieve that. If you double the wattage (and size the motor/prop accordingly) now it could climb two feet in one second.

not watts, but thrust which is Watts \ horsepower times the efficiency factor of the prop [which for us will always be a guess]. Yes a higher watt motor should swing a bigger prop faster and produce more thrust, but not always; particularly if the tips go sonic [ due to rpm and forward speed] or you lose motor power conversion efficiency [ faster you spin a motor, the more back EMF cancels forward current flow]. However all things being relative, watts works as a shortcut because it is the only available published value for a given motor.

 

[SSgt Duramax]

not watts, but thrust which is Watts \ horsepower times the efficiency factor of the prop [which for us will always be a guess]. Yes a higher watt motor should swing a bigger prop faster and produce more thrust, but not always; particularly if the tips go sonic [ due to rpm and forward speed] or you lose motor power conversion efficiency [ faster you spin a motor, the more back EMF cancels forward current flow]. However all things being relative, watts works as a shortcut because it is the only available published value for a given motor.

It is, the only think I think is missing from it is there is a huge difference size, weight, performance, and prop options between a 500 watt 2000kv motor and a 500 watt 750kv motor. One will be good at swinging a smaller prop and making the plane go fast, and one will be good at swinging a huge prop and making tons of static thrust. Not that I think folks in this discussion don't know the difference, but people trying to learn about the stuff might not.

 

[telnar1236]

Just to add on to the limits of algebra, there are not any closed form solutions to most of the math used in aerodynamics so you either need a stupidly powerful computer to do CFD or you just need to test as everyone else has been saying. Hand calcs will get you in the ballpark but won't get you much further.

That said, there is a whole set of equations used to compare aircraft of different sizes. I won't go in detail but it gets messy very quickly when doing so and you could easily spend months trying to calculate metrics for comparison.

The best measure of how different power setups will perform would be the ratio of excess power (power not needed to overcome drag and not lost when spinning the prop) to weight across the airplane's speed range. Of course, for this you need a good approximation of the drag coefficient, and a good thrust curve for the propeller-motor combination that accounts for the motor dynamics (this one is not too hard to get as brushless motors are pretty predictable up to near their top speeds so you can approximate using a straight line). Two airplanes with the same value at the same speed will accelerate or climb similarly at that speed, and if two curves are similar, the two aircraft should also behave similarly. Beyond what I want to do for an RC plane, but it should be a valid approach.