Just learned something new today and thought I'd share with other non-engineer trained, left brained people out there. This will be old news to the engineers/experienced builders/savants, but anyway...
A friend is scratch building a 75% SE5a replica from plans and we were talking about his planned engine (O-235/135hp) compared to the original Hisso that put out 200hp and gobs of torque. He mentioned the engine will be fine because his 75% airplane will weight less than half of the full sized airplane and my political science trained brain exploded. Common sense told me it would be a linear change (a 75% scale would weigh 75% of original) so I went looking for the reason why I was wrong.
Turns out something called the "square cube law" is the cause. When you change an object's scale, the new overall surface area is proportional to the square of the new scale, but the new volume/mass is proportional to the cube of the new multiplier.
So volume/mass changes exponentially against changes in overall scale.
Here's the math: If you have a simple cube with 1 foot sides, the total surface area is 6 square feet and the volume is 1 cubic foot. If you double the size (200% scale), the new surface area is found by multiplying the original size by the SQUARE of 2, so you have (2x2) x 6 = 24ft2 surface area. The new volume is found by multiplying the original by the CUBE of 2, so you have (2x2x2) x 1 = 8ft3. Doubling the dimensions changed the surface area by a factor of 4, but changed the volume/mass by a factor of 8.
Back to my buddy's SE5a, the full size airplane's gross weight was about 1,950#. A perfect 75% replica would only weigh 42% as much as the original. (.75x.75x.75x 1,950), or 822#. So the little O235 putting out 67% of the Hisso's HP will be adequate.
A friend is scratch building a 75% SE5a replica from plans and we were talking about his planned engine (O-235/135hp) compared to the original Hisso that put out 200hp and gobs of torque. He mentioned the engine will be fine because his 75% airplane will weight less than half of the full sized airplane and my political science trained brain exploded. Common sense told me it would be a linear change (a 75% scale would weigh 75% of original) so I went looking for the reason why I was wrong.
Turns out something called the "square cube law" is the cause. When you change an object's scale, the new overall surface area is proportional to the square of the new scale, but the new volume/mass is proportional to the cube of the new multiplier.
So volume/mass changes exponentially against changes in overall scale.
Here's the math: If you have a simple cube with 1 foot sides, the total surface area is 6 square feet and the volume is 1 cubic foot. If you double the size (200% scale), the new surface area is found by multiplying the original size by the SQUARE of 2, so you have (2x2) x 6 = 24ft2 surface area. The new volume is found by multiplying the original by the CUBE of 2, so you have (2x2x2) x 1 = 8ft3. Doubling the dimensions changed the surface area by a factor of 4, but changed the volume/mass by a factor of 8.
Back to my buddy's SE5a, the full size airplane's gross weight was about 1,950#. A perfect 75% replica would only weigh 42% as much as the original. (.75x.75x.75x 1,950), or 822#. So the little O235 putting out 67% of the Hisso's HP will be adequate.
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