I think I had a similar thought about wing loading. Why does it seem to go up with size? This is because the volume of the plane goes up by the cube of the increase in linear size and area only goes up by the square of the increase. eg. a plate of 12x12x1 has a volume (density/mass) of 144 or volume/area of 1. So double the size and you have 24x24x2 and a volume (density/mass) of 1152 (cube of the increase is 8) or a volume/area of 2. (Notice no units.) This has nothing to do with Reynolds number, inches, feet, pounds or how it flys, it is simple scaling and math.

I think the standard "wing loading" is meaningless without with scale and a more appropriate "flyability" number would be volume loading as stated by several people.

These various number exercizes are all nice.
The very basic - "ounces per square ft" is simple and the most widely accepted -and gives quick insight as to probable, low speed performance .

Gordon,

It always assumed that an airplane size (scale, whatever) is known when discussing wing loading. It is like discussing sex without saying if the object of discussion was a man or woman.

It is incorrect to think of the number as a "volume" as indeed the volume inside of an airplane is quite independent of the wing area.

The response of a wing to air has everything to do with Reynolds number - if it doesn't then all of the work I have done over a lifetime matching wind tunnel Reynolds numbers to data goodness has been pretty well wasted!!

I agree with Dick that in terms of model work ounces per sq ft is a good rule of thumb to use but again it does need a airplane size to go with it. Terms like .40 or .60 powered, hand launched gliders, parkfliers, pattern, scale, giant scale, etc. all immediately bring to the mind a relative size and wing loading that works nicely.

I shouldn't have implied that the Reynolds number doesn't mean anything. I just meant that it has no effect on the actual calulation of volume load.

But I do think that a volume load (or something that takes into account the size of the plane) simplifies the information better than area loading PLUS the size of the plane. It's sort of like describing an engine that make so much torque at a certain RPM. You can consoladate that information into a single power figure instead. If you really want all the details of that engine you need to look at it's entire power band, but a quick power figure gives you a good idea.

I am new to airplanes and I found it kind of confusing why wing loading number seemed to get higher the bigger the plane got and now that I understand why that's happening, it just makes sense to me to have a load number that is more like comparing apples to apples even with different size planes. I don't want to have to remember that 10oz/ft^2 is good for a .40 size and 25oz/ft^2 is good for a 50cc size. And I suppose you could even take it to another level and include the Reynolds number in the calc to more accurately predict the planes performance. And for me, at least, I want to use that information to predict it's low speed performance.

Off the top of my head all you would really have to do is just divide the conventional wing load by, say, the wing span, to "normalize" the load value for any size plane, roughly.

So how does this apply to the old ballistic 60-size pattern planes?

The reason that I am asking is because I am currently designing a 1/6 scale Pilatus PC7. I have drawn and figured out the wing plan
Wing span = 68 inches
Square inches = 712
Square feet = 4.95

Using the formula above and if I can keep the plane at 8 pounds I get
Wing Loading = 25.88 ounces/Square foot
WVL = 11.63

The size of this will end up being close to the ballistic pattern planes. All of this is if I can keep the plane at 8 pounds with retracts and struts, split flaps, etc. Current engine idea is the ST90.

Any thoughts?

Have been reading this thread and so I decided to figure out the wing loading on an Edge I am building, It has a wing area of 1200 sq. in. and my weight will be 231 oz's which will give me a wing loading of 27.8 or 28 oz's . Will this be a floater or a lead sled?

what do you think?

Thanks

From what I've been reading on RCU, it should be right in between the two extremes you described. Just right.

Marl

Well, nowadays, that's almost a lead sled. It really depends on your flying style. Take the hangar 9 Funtana 90 as a close example. It has 1108 sq.in.(7.69sq.ft) of wing area, and weighs about 8.5lbs, average, or 136 ounces. That figures to be a 17.7 ounce wing loading. Personally, for my flying style, if I had a 14.5lb plane with a 1200sq.in. wing area, I know I wouldn't like the way it flies, but that's just me.

meeka - for IMAC flyting - the 27 oz loading is just fine -on 1200 squares -
use an engine which will crank a 22x8 at least 6500 - you will be in good shape
for aggressive 3D crapola - lighte would be better -
we kep our 3D stuf that size - down in the low twenty's or high 19.
My 3D Petrol Petrel weighed 11 lbs was 1280 squares - ZDZ40 - very agile!

Thanks Dick, I am using a ZDZ 40 on this plane and it will be my IMAC plane. This will be my first attempt at IMAC, will be doing basic. The wing span is 79", When I had the glow engine on this plane my wing loading was 23.5, which was nice for landing, it actually floated to much. I crashed it after a bad thumbs incident, I liked the plane so much that I decided to build another but with a gas engine in it for IMAC, I choose the ZDZ 40 after seeing my friend put one in his 25% extra by great planes. I am doing everthing possible that I know of to keep the weight down. I am using a carbon fiber spinner, wing tube and landing gear. I am also using lithium batteries which I had in the first version and just 4 JR 8411 servo's with pull-pull for both elevators and the rudder. I selected a william bros pilot which is the lightest I could find (tough to locate one now that they are not making them anymore) and a 1oz. instrument panel which I need per IMAC rules. The plane itself is light but if anyone has any other ideas on how to lighten the plane please let me know, other than changing the engine and plane which are on my building table already.

Thanks All...

Hey Dick,

If you ever get a really bad airplane (or a good one) you feel like you want to really bug me with it then send the airplane to

Ben Lanterman
3432 Cov..................

You aren't buying this are you??

I tried.

Ben

Here is some ideas on lighter models
1 - I don't use any carbon fiber except fo once -on the Petrel-
no other carbon till I get to the lil electrics - then I use it .
I do evaluate every last part of the model tho - and you can't believe how much overbuilt stuff exists in kits -especially ARFS.
remember - the plane does not have to stronger than the weakest piece in it -
for example - the entire bare airframe for my old Buckers - weighed 6 lbs - 1800 squares - all up weight 16.9-(Tartan twin )-to almost 18 lbs (ZDZ80 single) -and there has never been any problem with strength.
The airframe is where you really save the weight - then put in only the pieces needed - no " beef it up" stuff .
On many of my models there is no engine mounting plate - just angle struts that attach engine to longerons .
It works for full scale ---

Dick I had always wondered about how the big 150cc engines fared on the front of some of the models. It's easier to visualize with a composite model, I guess we tend to think of them as stronger. But a really light built up airframe even if it is structuraly strong seems that it would vibrate apart. The only big engine I ever had was a Zeonah 35 or 45 or something like that on a World Engines Robin Hood. It had 1/4 inch thick ply sides and was built like a brick. Of course I put fiberglass over everything from the wing and landing gear forward. The motor shook like a wild creature and didn't ever get smooth.

I would guess the big twins might be smoother. I can see the airplane hanging on to the motor in the air but my mental airplane has the motor falling off when it lands.

With a full sized airplane you are tieing the motors into the steel tube structure which seems better able to handle the loads than something made of balsa.

What does your structure have to handle the loads of the motor and not shake apart?

Scaling laws are really interesting for modelers...it's a part of virtually everything we do. Often it's assumed that we're scaling from a full-scale aircraft but with so many variances in sizes these days we can apply scaling techniques within the confines of the models we fly.

The scaling of any general object must follow the "square-cube" law which defines (using my nomenclature) a change in scale by a change in a characteristic linear dimension.

If L1 is the length of the original object and L2 is the scaled version of that object then the scaling factor k is defined as:

k=L2/L1

You can derive the square-cube law by applying this technique to a simple geometry like a cube. You will see that the surface area of the cube will grow with k^2 and the volume of the cube will grow with k^3 such that:

S2=k^2*S1 (area)
Vol2=k^3*Vol1 (Volume) (mass, weight and force also scale with k^3)

If we apply this to our wing loading problem we start with a particular airplane with some characteristic length (typically the wingspan) which I'll call b. k is set by the ratio of the wingspans

k=b2/b1
likewise the wing area will grow with k^2 and the weight will grow with k^3 such that
S2=k^2*S1
W2=K^3*W1

If we define wing loading as W/S then we have k^3/k^2 = k so we know from the square cube law that :

(W/S)2=k*(W/S)1 This simply means that if you double the scale you can double the wing loading.

The reason for the so-called "cubic" wing loading also comes from the square-cube law. Modelers don't like to have to remember what wing loading is appropriate for their scale model so they find a figure of merit that works for all scales. This happens to be W/S^1.5 If you look at this using what we've already discussed you get that k^3/(k^2)^1.5 = k^3/k^3 = 1 so it's independent of scale.


You can play this game all over the place...for instance take the level flight linear velocity. The standard equation for lift is L=W=CL*q*S=CL*rho/2*V^2*S...assuming that air density and CL are independent of scale (which they aren't exactly...this is where Reynold number, Mach number and Froude number come into play) you find that V is proportional to (W/S)^0.5

Therefore velocity is proportional to k^0.5...this means that if you double the scale of the airplane the level flight speed increases by the square root of 2 or 41%.

Since we actually see scale speed as body lengths per second we can note that the time it takes for us to see the distance of one body length covered is given by

t=BL/V (body-length/velocity) we know that this is k/k^0.5 or k^0.5 so now we can see that

t2=k^0.5*t1 or stated differently, the model that's double in scale will appear to take 41% longer to cover this characteristic length.

This is quite interesting because the true linear velocity of the double-scale airplane is in fact flying 41% faster but appears to fly 41% slower.

You can also use scaling laws on power. If you say that the thrust required for level flight is approximately equal to D and that the power required is Drag*Velocity (D*V) you get the following:

P2=k^3*k^0.5 = k^(7/2) or k^3.5 This means that power required grows at a little faster rate than volume.

You can test this by scaling a 40% airplane down to foamy size. if the 40% has a span of 120" and uses a 16HP motor how much HP would an airplane of 30" require to have similar performance?

k=30/120 = 0.25 P2=0.25^3.5*16HP = 0.125HP or 93 watts (this is close to what we get running 12V at 8 amps.


You'll also notice that things like moments will scale with k^4 and moments of inertia will scale with k^5, RPM will scale as k^0.5 .....on and on.

The one thing to remember is the square cube-law knows nothing about aerodynamics and in many cases the aerodynamics can't keep up at the lower Reynolds numbers...in this case things like wing area have to grow to obtain similar performance.

George Hicks

Structure - good question--but first - I don't use either of those engines -
I do use singles -a lot --and except for a bit off idle firing pulse induced shake - they are very smooth.
My structures use L shaped spruce longerons top and bottom of fuselage - also the entire fuselage center is a sheet(s) of balsa which runs cross grain to the fuselage.
So imagine an I beam -on it's side.
The engine bearers are angled from the four engine mounting ears to each longeron - forming a pyramid.
these pieces are also L in cross section and are mechanically locked to each longeron.
Th entire assembly is now a large rigid structure . No see saw action in these setups
big slabs of wood are worthless in terms of rigidity .
This is simply an old carry over from control line building .
Mass balance technique -
I never use that setup and my Bucker -- almost 15 years old -never a structural or joint failure .
The composite structures however have a finite life - just like a DeHavilland (?) Comet .
The extrmely brittle nature of the CF sets up fatigue in critical areas - some worse than others
For an electric powered model these are a great match!
my 40 cc tuned pipe Petrel -- 11 lbs flying weight . 1280 squares
Almost all gas wood kit structure follows same old setup - a square motor box to a wing tube - also a non triangulated fuselage structure , which in the forward section relies on the square motor box locked to the tube and sheet sides to carry the load -
easy to do but not the swiftest setup
.