Weight/thrust/wing area-shape formula

[jconwell]

I've recently gotten into scratch built micro planes, and am having problems with getting planes that are too heavy for the engine (i guess).

does anyone have a one stop shop explanation about how to calculate wing area and total weight for a given engine thrust, so that it'll fly?

does this make sense?

[Rodney]

While this does not help you with engine size, it definately is handy for weight/versus wing area. Using the formula
wingvolumeloading= weight of model in ounces devided by wing area in square feet raised to the 1.5 power
if the answer falls between 7 and 10, flight should be rather tame, acutally a figure of 7 gives a real floater. 11+ becomes a flying brick. Restating the formual
WVL=(ounces/area)^1.5 using units mentioned above

[Tom Harper]

j,

Rodney gives an interesting approach. I'll have to try it.

An important consideration when dealing with small models is the fact that wing loading scales as the ratio of linear dimension. So, for models of similar configuration, a span of 48" may perform well with a wing loading of 14oz per square foot. A scaled model of 24" span will give similar performance at 7oz per square foot of wing area - half the size = half the wing loading.

For a 6:1 aspect ratio the first model would have an area of 2.7 sq ft and would weigh 2.7*14=37 oz. The second model would have an area of only .6 sq ft and would have to weigh .6*7=4.7oz for similar performance. The ratio of the weights is the cube of the ratio of linear dimension. So a ratio of 2:1 in linear dimension requires a difference in weight of 8:1 (4.7*8 ~ 37).

There are too many unknowns to allow practical calculation of performance. I have found the scaling equations to be of greater value.

For engine size, you need 50 watts per pound minimum, 100 watts per pound to be comfortable and 200 watts per pound to impress the guys at the flying field. Many tiny electric 3D models are approaching 200 watts per pound.

[BMatthews]

It's quite complex since it's based on more than just simple thrust unless you're talking about climb only. Direct drive solutions with small props with low pulling power but high prop wash speeds confuse the issue.

Your best bet is to run the numbers through one of the better electric model performance calculators. That'll suggest what the motor and prop performance will be like.

But there's also the wing loading that comes into play to determine the model's flying speed and stall speed. Here it's almost impossible in my books to make a model that is TOO light. But there is a good range of wing loadings for each size range. This is because of the old Reynolds number effect that is sometimes called the scaling effect. It basically means that as the model gets smaller the air acts differently and that means the model needs to have a lower wing loading compared to the bigger stuff to fly well.

What is acceptable will depend on what size you're talking about and what flying speed you're hoping to use.

But it sure sounds like you just need to build lighter.