Empty Weight Fraction

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The last thing we need to do before estimating gross weight is to figure out the empty weight fraction. So how do we do that?

Well it turns out that there is a relationship between the empty weight fraction (y-axis of the graph below) and the gross weight (x-axis) of airplanes. Here we’ve plotted a variety of composite airplanes (red) and aluminum ones (blue). If you want to try this yourself, click here to play with it on a graphing calculator.

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The curved lines correlate and like this:

$$\scriptsize a=\frac{W_e/W_0}{W_0^{-0.09}}\>\> \text{ or }\>\> \frac{W_e}{W_0}=aW_0^{-0.09}$$

The big idea here is to choose a reasonable a value for our plane, which we’ll use in a while to arrive at .

We have two data points of particular interest in the graph above. Look at the RV-14 (which we noted earlier has similar mission requirements to ours, although it’s an aluminum plane) and the DarkAero 1 (which has slightly different mission requirements from ours, but makes use of molded advanced composites, like we want to). We’ll use their a values to inform what we select for a.

Our plane likely won’t achieve the extremely low weight of the DarkAero 1 for several reasons:

• They’re making use of advanced manufacturing techniques,
• I’m just an ordinary guy interested in design and not a trained engineer, and
• the DarkAero is stressed as a normal-category airplane, while we’ll be using a higher ultimate load factor (“g-rating”) for reasons we’ll discuss another time.

Still, we want to place an emphasis on weight reduction by:

• Keeping the wing weight down by using pultruded graphite rods (which have an incredible strength-to-weight ratio) in the spar construction,
• selecting a light engine (currently we are considering the ULPower 520is, which is 50+ pounds lighter than traditional engines of similar power), and
• making use of molded and vacuum-bagged carbon fiber sandwich structures where it makes sense. (Later, when we get into detailed weight estimation, we’ll need to evaluate the cost for weight savings.)

So we’ll split the difference of the more-conventional RV-14A’s a=1.2 and the DarkAero 1’s a=0.97 and select a = 1.1. (The higher number we select, the higher the empty weight fraction will be.)

Revisiting the empty weight equation above, and inserting a = 1.1, we find:

$$\scriptsize \frac{W_e}{W_0}=aW_0^{-0.09}$$

$$\scriptsize \frac{W_e}{W_0}=1.1 \cdot W_0^{-0.09}$$

So now we have the empty weight fraction… or do we? Notice we still need to know to calculate . We’ll solve that problem in the next post and arrive at gross weight.