# If I were to build a J3 cub twice the size of the original using the same CG would it fly?

• How big of an engine would I need, if the original is 65hp?
• What would be the weight of the up-scaled plane? Simply twice the weight?
• What would be the stall speed?
• How fast would it go? 75mph?
• Is there a software program to test aircraft design?
• This isn't exactly a duplicate, but there's a lot of relevant information: What are the physical laws for upscaling an RC model to 1:1? – Greg Hewgill Jun 27 at 2:07
• 3 good answers from 3 smart people give 3 different HP ratings: 320, 520 (minimum) and 735. There's a lot of math and physics involved and simple "back of the envelope" scribbling won't get you accurate answers! – FreeMan Jun 27 at 13:14
• @Freeman Very right you are. Of course it is possible to construct larger aeroplanes than the J3, we see them flying around very regularly. Point is that linearly amplifying all dimensions does not work, the larger plane needs to be re-engineered with all the design choices and computations that come with that. – Koyovis Jun 27 at 14:06
• @Freeman remember power requirement hinges on weight and drag. The weight factor is more difficult to predict without detailed analysis, as it will hinge on strength requirements AND additional fuel/cargo/pax. A faithfully scaled (2x) J3 will need to go around 40% faster. I would go with 8x power as an off the cuff. The 74 foot wingspan Ford Trimotor weighs in a good reference, sporting 3x300 hp to lift around 10,000 lbs and cruise at around 100 mph. The design matches the J3 very well. (Late 1920s). – Robert DiGiovanni Jun 27 at 19:04

Unfortunately a simple scale-up would fall victim to the square-cube law: all dimensions times two means the volume and weight are 2x2x2 = 8 times the original, while the wing area is 2x2 = 4 times the original. It is the wing area that keeps the aeroplane up. It is the reason why birds cannot get any larger than they already are.

Someone in the 1920s analysed this and predicted that the maximum size for aeroplanes would be about that of the DC-3, but improved technology has proved that prediction wrong. A B777 has a way higher wing loading than a DC-3 of course. The square-cube law is not a law, it can be defeated by engineering. Point is that linearly amplifying all dimensions does not work.

How big of an engine would I need, if the original is 65hp?

Minimal: 8 x 65hp = 520 hp. We need a serious amount of extra thrust.

$$D = C_{D0} \cdot \frac{1}{2} \rho V^2 \cdot S + \frac{2 W^2}{\pi A e \cdot \rho V^2 \cdot S} \cdot$$

• $$C_{D0}$$ would stay the same if everything is scaled up
• S = wing area = 4 times as high
• W is 8 times as high.

$$D_2 = D_1 \cdot (4 + 8^2/4) = D_1 \cdot 20$$

So you need 20 times as much thrust at the same speed.

Increase V and the first factor increases, second factor decreases. There are of course many optimisations possible (weight saving, wing loading increase etc), but that goes beyond the scope of the question.

What would be the weight of the up-scaled plane? Simply twice the weight?

Eight times that of the original.

What would be the stall speed?

Higher than that of the original because the wing loading is higher. Depends on the flaps & slats installed.

How fast would it go? 75mph?

Yeah it might..but it would probably need to go faster as @xxavier mentions.

Is there a software program to test aircraft design?

FlightGear is an open source flight simulator that allows you to link your own flight dynamics model into it.

• Comments are not for extended discussion; this conversation has been moved to chat. – Federico Jun 30 at 12:30

In general, the power required by an airplane is proportional to its weight times its speed. The weight scales with the cube of the linear dimension, so the bigger J3 would weigh $$2^3 = 8$$ times more. Since the airspeed is squared in the formula for lift, the exponent for the proportionality of lift should be 1/2.

Now you have two powers for the scaling, 3 for the weight (or mass, in this case) and 1/2 for the speed. As the weight and speed are multiplied in order to get the proportionality of the power required, I add the exponents, and the result is that the bigger J3 plane would need an engine of $$2^{3.5} = 11.3 \times 65 = 735$$ hp.

Concerning the stall speed, and as airspeed scales with a power of 1/2, and the scale factor is 2, if the 'small' J3 has a stall speed of –say– 50 mph, you'll have a stall speed of $$50 \times \sqrt{2} = 71$$ mph for the 'big one'... The cruise and maximum speeds will also scale with $$\sqrt{2}$$...

Of course, all these are rough estimations... To start with, the weight does not grow exactly with the 3rd power of the linear dimension...

Yes, it would fly.

Scaling up a successful design has worked well in the past. Just two examples:

1. When Howard Hughes wanted a fast airliner for his TWA airline, he turned to Lockheed and asked them to design one on the basis of the wing of their P-38 fighter. The result was the Lockheed Constellation (the picture below shows the military version C-69).

1. In the summer of 1940, Willy Messerschmitt was asked to design a cargo glider with the payload bay the size of a Reichsbahn cargo car. He used the largest aircraft he had designed so far, the M-20, and scaled this up. The result was the Me-321, which was a considerably better design than the analog Junkers design Ju-322, which was designed from scratch and turned out to be uncontrollable.

What would be the weight of the up-scaled plane? Simply twice the weight?

No, it will be much heavier. The structure will have to be beefed up for the same reason that an elephant needs big, sturdy legs while an ant can use spindly legs and still carry a multiple of its own weight. Normally, this factor is the length factor by the power of 2.3 or 2.4. Since the aircraft will be hollow on the inside, simple cube laws which apply for solids will give too high a value.

If you look at existing aircraft, you will find that wing loading increases with size. That makes sense: The wing of an aircraft twice as big as the original will have four times its area. Its mass, however, will be five times bigger according to the exponential weight growth.

Engine size should be selected so the power to weight ratio is maintained. Your twice-as-big Piper J-3 will need 320 hp to be useable.

Since it is bigger and has a higher wing loading, the upscaled J-3 will also fly a bit faster. Stall speed will be 10 - 12% higher due to the higher wing loading. Friction drag will be smaller relative to its wetted area since it flies at a higher Reynolds number. The higher wing loading will again result in higher maximum flight speed, if only because the optimum point of lowest drag is at a higher dynamic pressure. But don't expect too much: I would expect that the top speed is just 8% higher. Maybe 10% if you are lucky.

Is there a software program to test aircraft design?

Yes. Many. But no freeware.

• The Constellation does not look like a linear upscale of the P38...of course upscaling is possible, with many technological changes and optimisations. – Koyovis Jun 27 at 8:14
• @Koyovis Look again. Look at the shape of the wing and stabilizer, the shape, size and position of the outboard fins and rudders. The center fin and rudder were probably added to account for using four engines (and the possibility of a failure much further outboard) instead of two. – Zeiss Ikon Jun 27 at 11:17
• @Koyovis: Only the wing was used for upscaling (obviously). – Peter Kämpf Jun 27 at 11:38
• @Koyovis I see one each. The P-38 tail booms weren't transferred over because the fuselage of the Connie was longer for cargo/passenger capacity. – Zeiss Ikon Jun 27 at 13:40
• @ZeissIkon Ah really? So they were different? – Koyovis Jun 27 at 13:53

Back in 1973, Air Progress magazine published an article on a proposed three times scaled-up Piper J-3 Cub with 500 hp, original top speed, 200 mile range, etc. You can find the article at:

http://sbiii.com/cyclops/stmott-3.html#kngkngcb

• Nice find. The author realises that construction methods must change, and that the MTO must be drastically limited, which is the main challenge. ... so we've decided that the wing construction should be a little different from the normal J-3's. By using plywood to cover the wing... Since we don't want to lose that good old Cub fee1, the wing loading must remain just as it is on the normal airplane, around 6.8 pounds per square foot. This gives us a maximum permissible gross weight of 10,924.2 pounds. – Koyovis Jun 27 at 22:37
• Wow! Thankyou for all the reply's, I have learned a lot so far. I am going to have to learn some more math I can see. there is enough info here to get me started Thankyou! I am going to have some more question later, after I do some math caculations. – Dreamer Jun 27 at 22:44
• @Dreamer It is of course possible to construct an aeroplane twice the size of the J3 and that looks like the J3 from the outside. And the weight won't be 8 times to start with, that is only the case if all dimensions are scaled up with factor 2. – Koyovis Jun 27 at 22:49
• @Koyovis - your bit of the quote about keeping the wing loading at about the same weight/area ratio is the key to success if this were a real project. Modern materials, etc. - assuming of course there is a (super extra large) budget for it – ivanivan Jun 28 at 20:37

The Piper Cub J3 is an excellent place to start in aircraft design. It represents all that was learned in the first 40 years of aircraft design as a tractor driven high wing mono plane with a properly proportioned and placed vertical and horizontal control surfaces. It is no accident this was the first trainer aircraft for many aviators.

Undoubtedly this design can be scaled up, but beyond the actual build it may be beneficial to look for the J3's attributes in other larger aircraft. The high wing gives improved stability in pitch and roll. This is a plane that wants to stay "upright". Now look at the 132 foot wingspan C130 Hercules cargo plane. Yes, a lot of Piper Cub there. And that large tail keeps it steady and can handle a wide range of CG.

So, for your scale up, plan on needing more power, and high lift devices such as slats and flaps to keep landing speed at a minimum. Also, evaluate strengthening requirements for fuselage and especially the wing to bear the heavier loads. And check out existing designs in the size range you desire.

And if you are really motivated, here is another Hercules, the Hughes H-4, aka "Spruce Goose". At 320 feet, it's wingspan is more than 9 times that of the J3. See if you can pick out the similarities.