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Minimum energy to height

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Minimum energy to height

Old 26th Nov 2021, 10:37
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Minimum energy to height

I'm playing with some concepts about minimum energy to height (basically I'm interested in achieving best altitude gain with battery electric aeroplanes that have very limited and heavy onboard energy storage).

Can anybody point me at any useful theory / papers / best practices on determining profiles for best height with minimum energy expenditure in aeroplanes.

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Old 26th Nov 2021, 15:51
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Not sure if it will be of any use,


South African built glider with an electric self starter motor.
They may have useful information.
Their performance is impressive, start and climb to 500mtrs then something like another 1.5 cruise battery power.
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Old 26th Nov 2021, 16:16
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Thoughts re specific excess energy:



Map Ps ( appropriate value of energy - electrics ) against altitude, then ‘fly the ridges’ ?
No concern about variable mass as with fluid fuel.
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Old 27th Nov 2021, 21:28
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Thanks both, looks from that, that I need to hit the equations myself regardless, but that Florida Tech MSc dissertation particularly contains some useful material.

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Old 13th Dec 2021, 19:34
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Doesn't a focus strictly on "minimum energy to altitude" without addressing distance travelled give the wrong optimisation for an aeroplane that wants to actually go somewhere ... a very steep path may be more efficient to altitude in some cases, but if you then have to make up the distance deficit in level flight, it may not be an overall benefit to the flight efficiency. (But recognizing that in practice for traditional aircraft, the altitude effect usually wins out anyway)
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Old 14th Dec 2021, 12:32
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That will depend upon the mission. A lot of the present electric aircraft projects focus on a training or sports role for the aeroplane, for which getting to a workable height to do whatever it is the pilot wants to do, so doing so with as much energy as possible once there is very helpful.

Clearly for A-B/transport missions, then yes, it's going to be a more complex set of problems to solve, but actually solving energy to height first isn't a bad starting point for tackling those also.

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Old 20th Dec 2021, 09:39
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Power Requirement to Keep a Jet Aircraft in the Air

The total energy of an aircraft flying in the atmosphere can be calculated using equation 1. [2]
E = ½ m v2 + mgh
A Boeing 737-300 has a maximum takeoff weight of 5.65 × 104 kg, a cruise altitude of h = 10,195 m, and cruise speed of 221 m/sec. Inserting these numbers into the above equation, we obtain 7.03 GJ for the energy at cruise conditions. [3] However, the engines mounted onto the wings of the plane are required to provide additional energy per time, power, in order to keep the aircraft flying at a constant altitude and speed. This extra power needed to overcome the drag acting on the airplane and is calculated using
P = (dh/dt) m gConsult a complete article. I hope it will be helpful. ThanksSource: large.stanford.edu/courses/2013/ph240/eller1/
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Old 28th Dec 2021, 18:00
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Error there somewhere, as 587kg for a 737 might be seen as a little on the light side.
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Old 28th Dec 2021, 21:16
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maximum takeoff weight of 5.65 × 104 kg

Obvious typo 5.65 * 10^4 makes a bit more sense
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