Reddit reviews General Aviation Aircraft Design: Applied Methods and Procedures

Oh boy, one of my favourite topcis! I'm doing something similar right now, trying to do some feasibility studies for an electric homebuilt! I'll try to answer to the best of my abilities, hopefully others on this forum.

My answer is based almost entirely on this book: General Aviation Aircraft Design: Applied Methods and Procedures and a little more on Simplified Aircraft Design for Homebuilders. The math isn't too tricky, though it helps if you have some background in aerospace or aeronautics. There are some pretty decent courses on EdX if you want to explore those further.

The answer depends significantly on what you want your aircraft to do (slow 4-seater? fast 2-seater?), and some estimates on the shape of your aircraft. I'll summarize just the necessary parts for this question.

The other thing to note is: there isn't much different about how an electric aircraft flies, the only difference comes in when you need to calculate the range. In a typical piston aircraft, the fuel is burned off and weight goes down as the flight continues, which helps increase the overall range. For an electric, sadly, that's not an option (though electrics have other benefits!)

To find the range of an electric aircraft, you need to know the following things:

• The estimated max. gross weight of the aircraft (W)
  
• The estimated empty weight of the aircraft (W_e)
  
• The estimated payload of the aircraft (W_p)
  
• The desired cruise speed
  
• The desired cruise altitude
  
• Estimated wing-loading for the aircraft
  
• Some airplane-specific parameters like parasite drag coefficient and induced drag coefficient.
  
• The specific energy of your battery (how much energy per kilogram does it store?)
  
• The Thrust/Weight ratio for the aircraft (which determines how much thrust is required per kilo of the aircraft total weight)
  
  As you can see, the first several requirements are based on what you want: what are your requirements? The airplane-specific parameters, like drag coefficients, can be estimated using existing aircraft in the same class. Raymer's book has great resources for estimates for several parameters based on many comparable aircraft. The last few are calculated using some basic formula.
  
  Let's do a sample calculation (and you can check the numbers to make sure they're reasonable):
  
  
• I guess the max. gross weight of my aircraft is 3400lbs. This is on the high end for single-engine aircraft, comparable to the very nicely designed Cirrus SR-22. But I want to carry a lot of payload and batteries, so I need the max. gross weight. So, W = 3400
  
• The estimated empty weight of the aircraft, as per Raymer, is W_e = 1.15*pow(W,0.91) = 1880 pounds. However, this is for piston-engine aircraft. A piston engine is much, much heavier than an electric engine for the same HP. For comparison, the SR-22 has a 310hp engine, which weights 475lbs as per the spec sheet. For the same horsepower, an electric engine only weighs about 170lbs. So, the actual empty weight estimate is W_e = 1880 - 475 + 170 = 1575lbs. Not bad!
  
• The estimated payload of the aircraft: W_p = 800lbs. I want 800lbs for 4 160 pound adults, 40lbs of baggage, and 100lbs spare margin in case people are heavier than they claim.
  
• From the above estimates, I can calculate how much space I have left for my battery: W_b = W - W_e - W_p = 3400 - 1575 - 800 = 1025lbs.
  
• I want to cruise at 8000ft. Most aircraft's cruise numbers are stated for altitudes of 5000-8000ft, so this isn't too bad. The air density at this height is 0.001869 slugs/ft^3.
  
• I want to cruise at 120kts. Might seem slow, but for now it'll do. This is equal to 202ft/s.
  
• Estimated wing-loading: Wing-loading refers to how much weight is being supported by each square foot of the wing. So, you need to roughly guess your wing area. We can use a reference here, the SR22 has a wing area of 145 sq. ft. With a weight of 3400lbs, the wing loading is 23.4 lbs/sqft.
  
• Estimated induced drag factor: This represents how much drag your aircraft produces just for being in the air. It depends on the aspect ratio of the aircraft, which, again, for the SR22, is ~10, and the induced drag factor k = 0.042
  
• Estimated parasite drag factor: this represents how much drag your aircraft produces because of its shape. As per Raymer, an estimate for homebuilt aircraft is 0.0265. The RV-7 comes in at 0.0175, so 0.0265 is a "safe" high estimate.
  
• Specific energy: This is how much energy the batteries store per pound of weight. Obviously, the higher the specific energy the better for us! Today, the specific energy for most production batteries is in the range of 220-260Wh/kg. There are some reports of batteries up to 350-400Wh/kg, but let's stick with 250Wh/kg for now. With this specific energy, the battery capacity is E = Specific energy battery_weight_in_kg = 250 (1025/2.2) = 121136Wh = 121.1KWh
  
• Thrust/Weight ratio: This is calculated from a formula that uses air density at cruising altitude, the induced and parasite drag factor, etc. The actual formula is a little difficult to type out here, but for these parameters, the T/W ratio comes out to around 0.069.
  
• Required thrust: this is simply T/W W = 0.069 3400 = approx. 234lbs of thrust for cruise.
  
• Required power: this is the power the engine must put out to provide the required thrust. Assuming propeller efficiency is 0.9, this comes out to about 71KW
  
• Possible endurance: Our battery capacity was 121KWh. For an engine that consumes 71KW, this means about 1.7 hours of endurance.
  
• Range: Simply cruise speed cruise endurance = 120 1.7 = 204 nm.
  
  I have not typed out the formulae here, let me know if you'd like me to, I can do so later today after work. The biggest thing to note (that isn't mentioned here) is that aircraft geometry is extremely important. If you were to increase the wing-loading and the aspect ratio, your range goes up dramatically. For example, if I increase my wing loading to 34lbs/sq ft and the aspect ratio to 16, the endurance goes up to 2.2 hours! Of course, that has other penalties: higher aspect ratios mean longer wings, which can increase weight because they need to be long and strong. A higher wing loading means smaller wings, which means if you lose an engine and aren't able to maintain airspeed, that small wing might have trouble keeping you afloat. I think it also hurts the stall speed.
  
  Other note: this is for a conventional aircraft configuration. Electric aircraft should ideally exploit the properties of electric motors: that they can be extremely small! You don't need to have one massive engine up front, you can have several small ones on the wing. This reduces drag over the fuselage and increases the dynamic pressure over the wings, which in turn increases the lifting capacity dramatically. For reference, check out the X-57 Maxwell NASA is building using this concept (which they call "Distributed Electric Propulsion").

General Aviation Aircraft Design by Gudmundson

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Also, check out Nicolai and Raymer. You might also find Jane's all world Aircraft catalog useful.