Aerospace Max aircraft range - electric powered

1. Jan 12, 2012

mheslep

I'm trying to come up with some ballpark ranges for RC electric powered aircraft. The literature I find so far on range, like the Breguet range equation, seems focused on mass change from fuel consumption which is not the case in battery powered electric aircraft. So I thought I would start from scratch for my edification and invite sanity checks. McKay's reference, here, provided guidance. Below I've substituted terms convenient for my design.

Fundamentally, the maximum range is some optimal aircraft velocity x time aloft, and time aloft is the total energy carried divided by the rate at which it is used, i.e. power, corrected for the efficiency of the propulsion system:

R = Vopt x (Ebatt/P) x ε
where:
R = maximum range
Ebatt = energy capacity of the battery
ε = propulsion efficiency
P = power​

and since force is power / velocity:

R = (Ebatt/Fthrust) ε
for level flight:

Fthrust = Drag
Lift = mg

or

Fthrust = mg (D/L)​

where:
m = aircraft mass
g = gravity
L/D = well known lift to drag ratio, or the glide ratio.​

then
R = Ebatt x ε x (L/D) / mg
Ebatt = Cbatt x me
where:
Cbatt = battery specific energy
me = mass of battery​

let
fbatt = fraction of aircraft mass dedicated to the battery
and
me = fbatt m​

then
R = Cbatt x fbatt x m x ε x (L/D) / (mg)
finally:
R = ( Cbatt/g ) x fbatt x ε x (L/D)

The term fbatt x ε x (L/D) is dimensionless. The fundamental range dependent on just carried energy is C/g.

Next up, some numbers.

Last edited: Jan 12, 2012
2. Jan 12, 2012

mheslep

Li Ion batteries are just short of 1 megajoule per kg, so in SI units C=1e6, g=10, the 'fundamental' range of a Li Ion powered aircraft is C/g = 100 km (62 miles). That applies to any aircraft so powered, of any size and air frame BTW.

Now for the dimensionless bit, the parameters.

Propulsion efficiency:
ε = ηbatt x ηfan x ηemotor

Common efficiencies for the battery and the motor are ~93%. If a prop maxes out at 85%, I'm guessing a duct-ed fan w/ vanes can also hit 93%, making the overall efficiency a convenient ε=0.8

Glide Ratio:
Best powered aircraft glide ratio to my knowledge is the Virgin Atlantic Global flyer. The Flyer achieved an L/D = 37.

Battery mass fraction:
I don't know. Commercial aircraft like a 747 top off with f=0.5. I'm guessing I can stuff f=0.6 in the airframe.

This RC 'Global Flyer' design gives a multiplier of fbatt x ε x (L/D) = 17.8
so Rmax li-ion = 1780 km (1100 miles)

Last edited: Jan 12, 2012
3. Jan 12, 2012

jhae2.718

I have some literature on electric ducted fans that I think gives some expressions for range and endurance, but I don't have it with me right now.

4. Jan 12, 2012

OmCheeto

Buy a blimp covered in flexible photo-voltaic materials.

(sorry. just had to subscribe to my favorite topic. )

5. Jan 12, 2012

mheslep

I note 1 MJ/kg takes the electric Flyer from New York to Bermuda (774 miles). Lithium Sulfur has demonstrated 1.26 MJ/kg, which would extend Rmax to 1390 miles. Still wont' cross the Atlantic (Newfoundland to Scotland) at 1900 miles

Last edited: Jan 12, 2012
6. Jan 12, 2012

mheslep

Ah, a Lithium primary battery (no recharge) Li thionyl chloride goes to 1.8MJ => 1980 miles. Primary batteries are often low power density though.

7. Jan 12, 2012

mheslep

Look forward to it.

8. Jan 13, 2012

mheslep

9. Jan 15, 2012

mheslep

I see the glide ratio of some modern jets is 20:1. So to build an electric regional jet w legs of a 1000 mi (1700km), battery energy density needs to improve less than 2X, to 1.8 mj/kg: R=180km * .8 * .5 * 20. That is, as soon as an e motor comes along w the same specific power of a gas turbine fan engine (7kw/kg).

10. Jan 17, 2012

jhae2.718

I was mistaken, it doesn't have anything on range. There are some equations for static thrust, power required, though. Let me know if you want those.

The booklet is from 1977, and is "Ducted Fans for Light Aircraft" by R.W. Hovey.

11. Jan 18, 2012

mheslep

Thanks. That reference led me to another which cites Hovey.

http://books.google.com/books?id=Yc...ns for Light Aircraft" by R.W. Hovey.&f=false

By Piolenc and Vwright. They walk through a ducted fan design example which has duct efficiency at 0.9, fan efficiency at 0.9, for a total of 0.81, i.e. less than a prop at its best?