Max aircraft range - electric powered

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 = V_opt x (E_batt/P) x ε

where:

R = maximum range
E_batt = energy capacity of the battery
ε = propulsion efficiency
P = power

and since force is power / velocity:

R = (E_batt/F_thrust) ε

for level flight:

F_thrust = Drag
Lift = mg

or

F_thrust = mg (D/L)

where:

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

then

R = E_batt x ε x (L/D) / mg
E_batt = C_batt x m_e

where:

C_batt = battery specific energy
m_e = mass of battery

let

f_batt = fraction of aircraft mass dedicated to the battery
and
m_e = f_batt m

then

R = C_batt x f_batt x m x ε x (L/D) / (mg)

finally:

R = ( C_batt/g ) x f_batt x ε x (L/D)

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

Next up, some numbers.

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 = η_batt x η_fan x η_emotor

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 f_batt x ε x (L/D) = 17.8
so R_{max li-ion} = 1780 km (1100 miles)

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.

OmCheeto

Buy a blimp covered in flexible photo-voltaic materials.

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

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 R_max to 1390 miles. Still wont' cross the Atlantic (Newfoundland to Scotland) at 1900 miles

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.

mheslep

Look forward to it.

mheslep

Interestingly, I see an RC 'model' aircraft (i.e. less than 11 pounds) crossed the Atlantic for the first time in 2003, using 2.2 kg of fuel (Coleman stove fuel).

http://en.wikipedia.org/wiki/The_Spirit_of_Butts_Farm

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).

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.

mheslep

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

http://books.google.com/books?id=YcA...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?