Max aircraft range - electric powered

In summary: They conclude that a ducted fan design could theoretically achieve a range of over 1500km if the power required was kept below 9 kW.This RC 'Global Flyer' design gives a multiplier of fbatt x ε x (L/D) = 17.8so Rmax li-ion = 1780 km (1100 miles)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.Buy a blimp covered in flexible photo-voltaic materials.The booklet is from 1977, and is "Ducted Fans for Light Aircraft" by R.W. Hovey.
  • #1
mheslep
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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.
 
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  • #2
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)
 
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  • #3
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
Buy a blimp covered in flexible photo-voltaic materials.

(sorry. just had to subscribe to my favorite topic. :redface:)
 
  • #5
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
 
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  • #6
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
jhae2.718 said:
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.
Look forward to it.
 
  • #8
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
220px-Tam5.jpg
 
  • #9
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
mheslep said:
Look forward to it.

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
jhae2.718 said:
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.
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?
 

FAQ: Max aircraft range - electric powered

1. How far can an electric powered Max aircraft travel?

An electric powered Max aircraft can typically travel up to 500 miles on a single charge.

2. What factors affect the range of an electric powered Max aircraft?

The range of an electric powered Max aircraft is affected by several factors including the weight of the aircraft, weather conditions, air traffic, and the efficiency of the electric motor.

3. How does the range of an electric powered Max aircraft compare to traditional fuel-powered aircraft?

The range of an electric powered Max aircraft is significantly shorter compared to traditional fuel-powered aircraft. Fuel-powered aircraft can typically travel thousands of miles on a single tank, while electric powered aircraft are limited to a few hundred miles.

4. Can the range of an electric powered Max aircraft be extended?

Yes, the range of an electric powered Max aircraft can be extended by using advanced battery technologies, increasing the efficiency of the electric motor, and implementing regenerative braking systems.

5. Are there any plans to improve the range of electric powered Max aircraft in the future?

Yes, many companies and researchers are actively working on improving the range of electric powered Max aircraft. As technology advances and battery technology improves, we can expect to see significantly longer ranges for these aircraft in the future.

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