Question on Wing Loading & Model Weight Relationship

[Apivat J]

After reading Andy Lennon’s Basic of R/C Model Aircraft Design, I’m a bit confused when he said wing loading is one of the first things to determine when designing a plane. But how do you know what wing loading is suitable for what type of aircraft? Looking at the equation, I get even more confused:

Wing Loading = (Model Weight/Wing Area)*144

Say, we start with a 3-view of a scale WWII aircraft. The only thing you can get is the wing area. Weight of the full size aircraft would be irrelevant as the model version will be much less. So, with one variable given how do you solve the equation? It seems to me like wing loading is just an arbitrary number you choose to determine the weight of the aircraft given the wing area. But then, for a scale model, you can’t go about changing the wing area to accommodate the wing loading as it would spoil the look of the aircraft. The only possible variable is the weight. But again the weight of the components (engine, servos, etc.) is pretty much fixed. So, you may end up having to change the wing loading figure.

Hmmmm….I'm sure this is wrong and I hope I showed you enough confusion in my head. So, if anyone out there could point me in the right direction, I would greatly appreciate.

Thanks.

[vintage1]

In general you just build as light as you can.

Then you know what weight the power train is for a given power output, and its a question of solving some simultaneous equations to get the right watts per pound for the performance you want.

If the stall speed ends up over about 18mph, its too big, or too heavy :D

[Sail 'n Soar]

Apivat J,

Recommended first design rule of thumb is to use the established rules of thumb. You have a start to the answer to your question in your original post. To start with you should have a very good handle on the total hardware system weight, that is; motor, prop, radio system, battery. You should be able to estimate your airframe weight as a function of its area - the model's scale. What have you built before? What did the airframe weigh? Scaled, the airframe weight of a similar structure with similar proportions will be proportional to the wing area. Since the airframe weight will most likely rrepresent less than half of the total model weight, the impact of airframe weight errors will be relatively small, so don't fuss over this too much. You can also get a good indiation of airframe weight from the various e-zone posts, if you are contemplating a design beyond your construction experience.

The next rule of thumg relates prop speed to design stall speed (1:2.5 - 3). This will lead to two or three speed classes: geared motors, non-geared motors and ducted fans. Personally, preferring higher thrust to weight numbers and slower flight speeds, since switching to electrics I've flown only geared power systems.

1. Choose a battery/motor/gear box initial prop combo
2. Calculate approximate prop speed
3. From prop speed calculate design stall speed
3. Choose airfoil based on desired flight characteristics
4. Calculate CLmax from airfoil choice
5. Given CLmax and desired stall speed, calculate target wing loading
6. Calculate initial weight estimate from hardware weight and initial airframe weight estimate - a judgement call, but if all else fails, let airframe something around 50% of the hardware weight - or go by the total weight vs. prop/motor/battery weight rule of thumb.
7. From initial weight estimate and desired wing loading, calculate target wing area.
8. Given wing area, revise airframe estimate and repeat steps 6. and 7.
9. Check watts per pound to assure they are equal to or greater than your desired minimum - from another rule of thumb.

Since flight speeds vary with the square root of wing loading, you don't have to worry about getting it just right. Ten to 15% wing loading errors are generally lost in the wash. Total weight errors, however, will impact your rate of climb. Keep the watts per pound up and that shouldn't be a concern either.

[BMatthews]

Wing loading plays a critical part in any model design. There's no doubt about that. The acceptable wing loading range for models depends on....

1- the size of the model. 1/2A models require a much lighter wing loading than a 1/4 scale model to achieve comparable flight performance
2- the intended speed range of the design. Gliders require a lighter wing loading to fly slowly in their intended manner than a racing model does. So gliders are often very large compared to their weight.

In any design there are fixed weights of the radio and powerplant. Modelers must think ahead and select the gear to suit the model being built. For example micro gear for a light electric parkflyer. On the other hand if you are working with gear already on hand then you want to select a model size that will carry it well based on past experience or knowledge gained through analysing other designs.

Once you know what you have for a fixed weight and have selected a general size of model that such gear and engine is typcially used in then you can start designing the wing area and from that the size of the model for span, length and construction methods that will keep the weight within the target range. A major part of this is analysing the design as it takes shape and guessing at the weight.

Full size aircraft designers follow much the same path with the addition of the intended payload and fuel load to the equation. There's a lot of juggling involved to shape the design and keep the materials used to provide the structure under control.

[Apivat J]

Thanks guys. At least I start to see some light at the end of the tunnel.

This is my first time building some thing absolutly from scratch and the first time dealing with the aerodynamic stuff. I have built quite a few models from plans in the past. The nice thing about that is all you need to do is follow the specs and you'll be alright, your plane will fly. But scratch building present a whole new challenge. You have to work will lots of unknown. I feel I spent more time figuring out aerodynamic formulas and their relationships to one another than building the model itself.

By the way, I have just finished the model. It's a composite 1/10 scale P40E (42" Wing Span). It is powered by .32 glow engine although originally intended for a speed 600 type motor. In fact, today is its maiden flight and I've got all the aerodynamic stuff figured out. Actually, I should say the plane got it all figured out and it didn't take that long. Here're some pics

[Apivat J]

Sail 'n Soar,

Could you please elaborate on 2. Calculate approximate prop speed and 3. From prop speed calculate design stall speed?

Thanks,


BMatthews,

The acceptable wing loading range for models depends on....

1- the size of the model. 1/2A models require a much lighter wing loading than a 1/4 scale model to achieve comparable flight performance
2- the intended speed range of the design. Gliders require a lighter wing loading to fly slowly in their intended manner than a racing model does. So gliders are often very large compared to their weight.


So, it's naturally for a 1/10 scale model to have higher wing loading. Am I right? But "higher" is a relative term. In this case, when do we consider a wing loading high and when do we consider it too high or too low? What would be the impact on the model beside higher landing speed for high wing loading?

[BMatthews]

A lovely job there Apivat. It looks wonderful. And it's all the sweeter when it's your own design.

Higher is a relative term for sure. From my experience acceptable wing loadings to allow for a decent glide speed are in the 9 to 11 oz/sq foot for 1/2A sized 36 inch models. But for a 48 inch 450 sq in sport model with a 25 to 32 I'd be happy with about 16 oz/sq foot, ecstatic if it was 12 to 13 and troubled but not too worried if it was in the 18 to 19 oz/sq foot range. At that upper end we are talking about a 4 lb model with 450 sq inches. Not a trainer but with good aero design would be flyable if not a lot of fun. And yet a big third scale aerobatic bird would be running up around 35 oz per sq foot. Full size airliners have loadings up around 100 lbs/sq foot but their landing speeds are higher than our max speeds. Each aircraft size range has a happy zone for desireable wing loading.

You've flown your P40 I gather? Not a lot of wing area in a 42 inch P40 thanks to the taper. I'd be aiming at no more than a 14 to 16 oz/sq foot loading for that sort of size to ensure a decent landing speed and overall fairly friendly slow speed charactaristics. Granted some of the problems of a small heavy model can be helped by careful airfoil selection but it can only do so much. Certainly in this case engine power is not an issue. The 32 will carry a LOT more weight than the wing loading numbers imply but the model would start getting a bit nasty when slowed down or perhaps even snap stall out of really tight turns or loops. Some washout in the tips and a thicker airfoil can often help matters there. Watch those landings. Especially in a strong headwind. The reduction in the headwind speed as you settle in through that last 6 or 7 feet thanks to the ground shear effect will bite you that much easier with a heavy model than with a light one. Keep a bit of extra speed on and flare about 2 feet up and then hold it until it settles on it's own. Practice about three mistakes high... :D

So fess up. What's the wing area and overall weight? How does it seem to react when it's flying?

If it was me designing a model for a .32 and knowing what I know about wing area, power loading, and overall desired size for such an engine I'd probably shoot for about 400 to 425 sq inches for a P40. That would probably produce a model of about 45 to 47 inch span? The fuselage of such a model would have a fair amount of volume so some extra care would be needed to control the weight. Both careful wood selection as well as minimal structure.

[Sail 'n Soar]

Sail 'n Soar,

Could you please elaborate on 2. Calculate approximate prop speed and 3. From prop speed calculate design stall speed?



Befor answering your question, the .32 seems a little large for your 42" P-40. You must be more into power than relaxed flying.

Step 2: Relative to approximate prop speed, easiest way to find that is with one of the available software packages. I've been happy with MotoCalc, but there are other electric motor calculators, including free ones on the web. If you are REALLY into design, before discovering MotoCalc I had written my own calculator based on the published battery and motor constants and propeller theory. Personally, I won't waste my time going that route again!

Steo 3: Next is applying the prop speed vs. stall speed rule of thumb. Published guidance there is the prop speed should be between 2.5 and 3 times stall speed for good all round performance for all but powered sailplanes. For example, if the calculated prop speed for your motor/GB/propeller/battery is 45 mph, then your design stall speed would be between 15 and 18 mph. You really don't want to design to a higher stall speed because your flight envelope will be really limited, i.e., max vs min level flight speed. You can always design to a lower stall speed, but in that case there are most likely other prop combinations that will give you a higher thrust / better performance. Your aircraft is also larger and heavier than it needs to be, which will reduce your max rate of climb. For this case, your "propulsive efficiency" will be relatively low - wasting energy moving a lot of air around with little to show for it.

Step 4: Given design stall speed and your chosen airfoil characteristics, you can calculate design wing loading from W/A = rho*U^2*CL/2.

Hopefully my elaboration touched the details you wanted. If not, let me know and I'll try again.

Gerry

[Apivat J]

Thanks for your compliments, Bruce. I applied "the looks could kill" concept to the model and it works on many club members... ;) It generates lots of Hoo...Haaa there... :D But you guys caught me. :p

Indeed the .32 proved to be too powerful for the model. It generates tremendous torque so much so that it rolls the plane left as soon as it leaves the ground. Of course, it resulted in a crash on the first run. Before I go on, here's the spec. to facilitate our discussion (it's a bit shameful, though):

Wing Span : 42"
Wing Area :295 sq. inch (definitely too small)
Weight (AUW) : 57 oz
Wing loading : 27 oz/sq ft
Airfoil : Eppler 197
Root Chord: 9.64"
Tip Chord : 4.92" (Since the wing has rounded tip, the measurement is taken at the base of the tip. Is it correct?)
CG location is at 27% MAC
Decalage : +1 degree
Power : .32 Glow engine
Prop : Master Aircrew 10x6
Servos : S3001x2 (Elev, Rudd), S3107(micro servo)x3 (1 for Throttle, 2 on each side of the Ailerons)

I really envy you guys for having the ability to know the flight characteristics before you even build the model. I hope to reach that stage some days....soon. That will be a lot more fun.

On the secound run, I was too afraid to fly the plane so, I get the club instructor to do it for me. From my observation, the plane is tail heavy, too much torque, too much control throw so, it was very touchy. To manage the torque on take off, the power was set at 40-50% with almost full right rudder. Timing was critical as full right rudder was apply only when the plane rotate off the ground to offset the torque. The climb was maintained at 20 degree at 50% power. More power at this point would snap the plane to the ground. It was not a very enjoyable flight for the instructor after that because of the heavy tail. On landing, it stalled at about 3 feet above the ground. The plane went somersault on its wing. No major damage. It was as tough as as a bull!!

On the third run, I added 3 stones :D to the fuel tank compartment to bring the CG to 25% MAC. A part from having to cope with the torque on take off, the plane flew reasonably well. On landing, extra speed is needed to keep it from stalling. I'm not quite sure how fast it was but definitely "not-for-beginner" type of speed.

So, after your helpful suggestions and recommendations, I think there are two choices:

1. Re-scaled it to about 47" span.
2. Reduce any extra weight on the airframe and change the engine.

I think I'll go for choice 2 eventhough I'd never make it to the target wingloading of 16oz/sq ft. Do you think 20oz/sq ft will be ok? Also, I'm planning to change to power souce to electric. I have Magnetic Mayham reverse motor, 30A BSC, and 10xSCR1400 NiCd pack. What do you think?

Sail 'n Soar,

Thanks for your explaination. I downloaded MotorCal a while back but have never look at it yet. Maybe it's time to do so now.

BTW, I'm trying to figure out the abbreviation in the formula W/A = rho*U^2*CL/2 in step 4. Do they mean as follow?

W/A = Wing loading
rho = I definitely don't know this one
U^2 = Velocity square
CL = CL max

[BMatthews]

Well. I guess the facts follow the performance. *IF* you can get it down to 20 oz per foot it would probaby fly well enough to keep it around but it's never going to be a nice fun casual flying model that you can horse around with general impunity. It'll always have a snap roll or two waiting to spring on you if you get sloppy with it. I'm not sure how you'll lighten the model by a full pound without major surgery but if you can then more power to you. Bear in mind though that just putting in a lighter engine and battery in the nose won't do any good if you just have to add a lump of lead to balance it. You'll need to lighten the tail by enough that you don't need any nose weight with the lighter components. As you found out balance is critical even if it is overweight.

I'd forget about electric for this airframe. While it looks wonderful it's obviously quite solidly put together and the wing loading is only going to go up with an electric motor PLUS batteries. If it has nasty habits now it'll only be worse with more weight. I don't care if the motor can fly it fast enough. At some point you need to enjoy flying the model and not just tolerate it or what's the point?

At least you chose an airfoil that has the stuff to handle the weight decently. But as I mentioned the airfoil can only do so much towards masking the loading issue.

For that engine you definetley need more area. Using your span and area numbers I figure that a 1.25 times enlargement of what you have would bring the span up to 52.5 and the area to 460 (1.25^2 x 295) That would be a nice size wing but the fuselage would be HUGE. A decent compromise would be 1.2x enlarging for 425 sq inches. And with careful and lightweight oriented design and light materials you should be able to keep the weight to 64 oz or less and that would produce a nice flyer. The .32 are known as powerhouse engines so it should handle the size and 4 lbs or less total weight quite well.

All this knowledge comes through experience. You just need to put in more time and build more models. You'll soon develop a feel for what works and what doesn't and how YOU like to fly. You've learned a LOT out of this project so even if it never saw the air ever again it's been a fantastic success. Hey, it FLEW. You now have a better handle on many design and building aspects and where improvements can be made. For the next one use less and thinner woods, pick only the lighter stock (balsa has a much wider range of density than any other wood known, it's up to YOU to pick the light stuff) and you'll be sure of future success.

[Sail 'n Soar]

BTW, I'm trying to figure out the abbreviation in the formula W/A = rho*U^2*CL/2 in step 4. Do they mean as follow?

W/A = Wing loading
rho = I definitely don't know this one
U^2 = Velocity square
CL = CL max


I work in English units, for which:

W = weight in pounds.
A = wing area in square feet
rho = density of air (at standard atmosphere =.002378 slugs/ft^3 at sea level, 59 degrees F)
U = velocity in ft/sec
CL = coefficient of lift, primarily a function of the angle of attack. It's set to CL max when you are trying to calculate either the minimum air speed for straight and level flight or the max g's that can be generated at any speed.

At the beginning of this thread you mentioned Andy Lennon’s "Basic of R/C Model Aircraft Design". Firgure 2, Page 20, will give you graphically aircraft speed in miles per hour for wing loadings between 4 and 48 oz/sq ft.

[Sail 'n Soar]

Started refreshing myself in what is in Andy Lennon's book. Table 1, Page 23, provides his guidelines relative to 2-cycle engine power loading, wing loading and aspect ratio for model types between thermal gliders and high speed/highly maneuverable power ships. Substituting watts per pound guidelines for the 2-cycle power loading numbers provided in Andy's table, the chart is equally applicable for electrics.

If you down-loaded MotoCalc quite some time ago your free trial period is well past, so you'll need to pay the small fee to be able to use the program. But once you do you'll be able to run through all the electric performance trades discussed to first order. Your biggest challenge will be in defining realitstic airframe plus radio system weights for a given wing area. The program will also provide flight analysis "opinions" in terms of prop speed vs. stall speed, wing loadings, flight characteristics, etc. You needn't consider the opinions given as gospel, but they do highlight potential performance issues you need to consider.

[Apivat J]

Appreciate all your response. It straighten lots of things for me here. But one last question about that dreadful torque. Are there any other ways to manage it beside adding 2 degree right thrust? Are there any other design implications when the plane roll left as soon as it takes off?

[BMatthews]

Another degree may help tame it but what you have here is a huge engine for the size of airplane.

I suggest you follow the method used by the high powered prop fighters used in the later stages of WW2. Good speed before you lift off. If a Mustang pilot lifted off too soon the plane would respond just like your P40 and roll onto it's back. The key was to have proper speed before lifting off or all the rudder available would not do the job. Ailerons in this case will probably make things worse thanks to adverse yaw and possible stalling on the lowered aileron.

You'll probably find that just like the big ones you need to hold some right rudder for the initial climb but once up to speed it'll be OK.

[Marion]

Beautiful Airplane !!!!

[Apivat J]

Thank you Marion. It will be a lot more beautiful if it could lose some more weight. But, as Bruce said, it would be difficult. I agreed unless I cast the fuselage again with vacuum bagging technique. So, that one option. The other option is to rebuild the whole thing again (that would be my 4th time) with 450sq ft wing area and keep the structure as light as possible.