# Why battery-powered aircraft will never have significant range

### Help Support Homebuilt Aircraft & Kit Plane Forum:

#### Jay Kempf

##### Curmudgeon in Training (CIT)
Advertising is much more efficient at generating propulsive power.
Great sentence

#### Dusan

##### Well-Known Member
I have some Unicorn poop I am willing to sell you.
It is recommended for fertilising the antigravimetric field. The yeld of fools believing in this stuff will be higher.

#### pictsidhe

##### Well-Known Member
I'm going to annoy some of you with maths.
Let's take our hypothetical 'world beater' ecraft and see how it fares in reality

Flat plate area 0.15m2
Takeoff weight 200kg (oh come on, you can convert that!)
Altitude 46,000 (probable safe limit for pure oxygen breathing)
Air density 0.226kg/m3
Span 39' (11.9m)
Flat plate drag area 0.15m2 (about 1.5sqft)

Flat plate drag at altitude:
0.5 x 0.226 x 50 x 50 x 0.15 = 42.4N
Flat plate drag power
Drag x 50 = 2120W
With 75% propulsive efficiency
2120/0.75 = 2830 W

Induced drag, assumed span efficiency 0.8

200 x 200 x 9.8 x 9.8 / (0.5 x 0.226 x 50 x 50 x pi x 11.86 x 11.86 x 0.8) = 38.5N
Induced drag power
38.5 x 50 = 1920W
With 75% propulsive efficiency = 2560W

Total cruise power required at 46,000' and ~100mph = 5.4kW

3 hours of cruise = 16.2kW of battery
Zero batteries are around 180Wh/kg. So we'd need 90kg of batteries just for cruise. Better increase the T/O weight and recalculate.
400kg T/O weight, 70m/s. We now have 5,120W worth of induced drag and 7750W of parasitic drag. Total power for 100mph cruise is now 12.9kW. Uh, oh. Now I need 38.7kW of battery for 3 hours of cruise. 215kg of zero batteries. Good job I allowed so much weight!

Wait, I forgot climb!
14,000m x 400 x 9.8 = 55MJ
x propulsive efficiency = 73.3MJ
In kWh, 73300/3600 = 20.3kWh
Oh dear, better add on another 113kg of zero batteries.

I must be getting close now?
80m/s, 550kg
Parasitic power: 11600W
Induced power: 12100W
Climb energy: 27.9kWh

Ah, poop. Now I need 99kWh of batteries. That's 550kg of zero batteries.

Weight a minute. That's 100% of the aircraft weight. Nothing left for luxuries like wings and fuselage or motor. I suspect that I may be in a losing battle here? I have no clue how to build a 160mph aircraft that light.

Topspeed, could you please show me where my maths is wrong? I seem to have reached a cognitive impass.

#### blane.c

##### Well-Known Member
HBA Supporter
I'm going to annoy some of you with maths.
Let's take our hypothetical 'world beater' ecraft and see how it fares in reality

Flat plate area 0.15m2
Takeoff weight 200kg (oh come on, you can convert that!)
Altitude 46,000 (probable safe limit for pure oxygen breathing)
Air density 0.226kg/m3
Span 39' (11.9m)
Flat plate drag area 0.15m2 (about 1.5sqft)

Flat plate drag at altitude:
0.5 x 0.226 x 50 x 50 x 0.15 = 42.4N
Flat plate drag power
Drag x 50 = 2120W
With 75% propulsive efficiency
2120/0.75 = 2830 W

Induced drag, assumed span efficiency 0.8

200 x 200 x 9.8 x 9.8 / (0.5 x 0.226 x 50 x 50 x pi x 11.86 x 11.86 x 0.8) = 38.5N
Induced drag power
38.5 x 50 = 1920W
With 75% propulsive efficiency = 2560W

Total cruise power required at 46,000' and ~100mph = 5.4kW

3 hours of cruise = 16.2kW of battery
Zero batteries are around 180Wh/kg. So we'd need 90kg of batteries just for cruise. Better increase the T/O weight and recalculate.
400kg T/O weight, 70m/s. We now have 5,120W worth of induced drag and 7750W of parasitic drag. Total power for 100mph cruise is now 12.9kW. Uh, oh. Now I need 38.7kW of battery for 3 hours of cruise. 215kg of zero batteries. Good job I allowed so much weight!

Wait, I forgot climb!
14,000m x 400 x 9.8 = 55MJ
x propulsive efficiency = 73.3MJ
In kWh, 73300/3600 = 20.3kWh
Oh dear, better add on another 113kg of zero batteries.

I must be getting close now?
80m/s, 550kg
Parasitic power: 11600W
Induced power: 12100W
Climb energy: 27.9kWh

Ah, poop. Now I need 99kWh of batteries. That's 550kg of zero batteries.

Weight a minute. That's 100% of the aircraft weight. Nothing left for luxuries like wings and fuselage or motor. I suspect that I may be in a losing battle here? I have no clue how to build a 160mph aircraft that light.

Topspeed, could you please show me where my maths is wrong? I seem to have reached a cognitive impass.
You forgot the solar cells.

#### Dan Thomas

##### Well-Known Member
I'm going to annoy some of you with maths.
Let's take our hypothetical 'world beater' ecraft and see how it fares in reality

Flat plate area 0.15m2
Takeoff weight 200kg (oh come on, you can convert that!)
Altitude 46,000 (probable safe limit for pure oxygen breathing)
Air density 0.226kg/m3
Span 39' (11.9m)
Flat plate drag area 0.15m2 (about 1.5sqft)

Flat plate drag at altitude:
0.5 x 0.226 x 50 x 50 x 0.15 = 42.4N
Flat plate drag power
Drag x 50 = 2120W
With 75% propulsive efficiency
2120/0.75 = 2830 W

Induced drag, assumed span efficiency 0.8

200 x 200 x 9.8 x 9.8 / (0.5 x 0.226 x 50 x 50 x pi x 11.86 x 11.86 x 0.8) = 38.5N
Induced drag power
38.5 x 50 = 1920W
With 75% propulsive efficiency = 2560W

Total cruise power required at 46,000' and ~100mph = 5.4kW

3 hours of cruise = 16.2kW of battery
Zero batteries are around 180Wh/kg. So we'd need 90kg of batteries just for cruise. Better increase the T/O weight and recalculate.
400kg T/O weight, 70m/s. We now have 5,120W worth of induced drag and 7750W of parasitic drag. Total power for 100mph cruise is now 12.9kW. Uh, oh. Now I need 38.7kW of battery for 3 hours of cruise. 215kg of zero batteries. Good job I allowed so much weight!

Wait, I forgot climb!
14,000m x 400 x 9.8 = 55MJ
x propulsive efficiency = 73.3MJ
In kWh, 73300/3600 = 20.3kWh
Oh dear, better add on another 113kg of zero batteries.

I must be getting close now?
80m/s, 550kg
Parasitic power: 11600W
Induced power: 12100W
Climb energy: 27.9kWh

Ah, poop. Now I need 99kWh of batteries. That's 550kg of zero batteries.

Weight a minute. That's 100% of the aircraft weight. Nothing left for luxuries like wings and fuselage or motor. I suspect that I may be in a losing battle here? I have no clue how to build a 160mph aircraft that light.

Topspeed, could you please show me where my maths is wrong? I seem to have reached a cognitive impass.
Reality is hard for everyone. Math is hard for some. They consider it optional.

#### pictsidhe

##### Well-Known Member
You forgot the solar cells.
Ah poop, that would surely change everything!

#### Vigilant1

##### Well-Known Member
Ah poop, that would surely change everything!
Yeah. I'm eager to know how we get that very low (provided) drag number with a wing top surface covered with solar cells.
And if the math indicates thing don't work with zero structural weight, it'll be interesting to see how the induced drag from the weight of the solar cells "improves" things.
Time to think farther outside the box. "Pilot Bill, have you prepared for today's flight? Weather briefing? Mandatory meal of 2 kg of cabbage and beans? Okay, plug into the methane collector and feed that fuel cell. The low pressure at altitude will help get every last cc of energy. Good luck!"

#### pictsidhe

##### Well-Known Member
Yeah. I'm eager to know how we get that very low (provided) drag number with a wing top surface covered with solar cells.
And if the math indicates thing don't work with zero structural weight, it'll be interesting to see how the induced drag from the weight of the solar cells "improves" things.
Time to think farther outside the box. "Pilot Bill, have you prepared for today's flight? Weather briefing? Mandatory meal of 2 kg of cabbage and beans? Okay, plug into the methane collector and feed that fuel cell. The low pressure at altitude will help get every last cc of energy. Good luck!"
Bare solar cells could be built flush into a composite laminar wing. Curvature is limited.
More span and less speed would be the way forward. I have NFC how to build something with the necessary weight and speed at 70kg.

#### blane.c

##### Well-Known Member
HBA Supporter
Blimp, not the structure of a dirigible and like a balloon it may continue to expand with altitude.

#### Speedboat100

##### Banned
I'm going to annoy some of you with maths.
Let's take our hypothetical 'world beater' ecraft and see how it fares in reality

Flat plate area 0.15m2
Takeoff weight 200kg (oh come on, you can convert that!)
Altitude 46,000 (probable safe limit for pure oxygen breathing)
Air density 0.226kg/m3
Span 39' (11.9m)
Flat plate drag area 0.15m2 (about 1.5sqft)

Flat plate drag at altitude:
0.5 x 0.226 x 50 x 50 x 0.15 = 42.4N
Flat plate drag power
Drag x 50 = 2120W
With 75% propulsive efficiency
2120/0.75 = 2830 W

Induced drag, assumed span efficiency 0.8

200 x 200 x 9.8 x 9.8 / (0.5 x 0.226 x 50 x 50 x pi x 11.86 x 11.86 x 0.8) = 38.5N
Induced drag power
38.5 x 50 = 1920W
With 75% propulsive efficiency = 2560W

Total cruise power required at 46,000' and ~100mph = 5.4kW

3 hours of cruise = 16.2kW of battery
Zero batteries are around 180Wh/kg. So we'd need 90kg of batteries just for cruise. Better increase the T/O weight and recalculate.
400kg T/O weight, 70m/s. We now have 5,120W worth of induced drag and 7750W of parasitic drag. Total power for 100mph cruise is now 12.9kW. Uh, oh. Now I need 38.7kW of battery for 3 hours of cruise. 215kg of zero batteries. Good job I allowed so much weight!

Wait, I forgot climb!
14,000m x 400 x 9.8 = 55MJ
x propulsive efficiency = 73.3MJ
In kWh, 73300/3600 = 20.3kWh
Oh dear, better add on another 113kg of zero batteries.

I must be getting close now?
80m/s, 550kg
Parasitic power: 11600W
Induced power: 12100W
Climb energy: 27.9kWh

Ah, poop. Now I need 99kWh of batteries. That's 550kg of zero batteries.

Weight a minute. That's 100% of the aircraft weight. Nothing left for luxuries like wings and fuselage or motor. I suspect that I may be in a losing battle here? I have no clue how to build a 160mph aircraft that light.

Topspeed, could you please show me where my maths is wrong? I seem to have reached a cognitive impass.

I don't aim that high with a 68 kg empty weight motorglider. 30 000 ft and 110 kg of batteries...900-1200 watts minimum cruise power....climb possibly 2-3 kw.

Above is an image of an efficient electric aeroplane.

Last edited:

#### Vigilant1

##### Well-Known Member
900-1200 watts minimum cruise power.

#### Speedboat100

##### Banned

1.6 hp...tops.

750 watts is possible:

I wonder why it weighed 140 kg empty ?

Last edited:

#### pictsidhe

##### Well-Known Member
I don't aim that high with a 68 kg empty weight motorglider. 30 000 ft and 110 kg of batteries...900-1200 watts minimum cruise power....climb possibly 2-3 kw.

View attachment 104430

Above is an image of an efficient electric aeroplane.
I used the numbers you gave in response to a request for its specs. I guess you've now moved the goalposts to a lower altitude?

Show us the maths for any of your designs. I gave you a template to follow. I even resisted the temptation to derive equations for necessary span/weight/battery fraction, or check your flat plate area.

#### Speedboat100

##### Banned
I am still tweaking. I haven't weighed the material presicely. Plane is 2.6 meters shorter than Rochelt kite Solair 2.

#### pictsidhe

##### Well-Known Member
I am still tweaking. I haven't weighed the material presicely. Plane is 2.6 meters shorter than Rochelt kite Solair 2.
So the cruise power numbers you keep giving out are plucked out of thin air?
Why am I not surprised?

HBA Supporter
Blimp

#### Speedboat100

##### Banned
So the cruise power numbers you keep giving out are plucked out of thin air?
Why am I not surprised?

Well the neighbourhood is right.

#### pictsidhe

##### Well-Known Member
Well the neighbourhood is right.
Your neighbourhood is cloud cuckoo land?

#### Speedboat100

##### Banned
Your neighbourhood is cloud cuckoo land?

Are you trying to piss me off ?

If I have a plane that has half the mass of Solair 2 and better/lower wingloading and lesser drag..I am certainly at better performance than the arofementioned Solair 2. It is that simple.

Last edited: