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I am developing code for a fixed-wing aircraft in ArduPilot to control desired airspeed and vertical speed through attitude commands (roll, pitch, yaw, and thrust) in simulation.

I understand the following:

1.Vertical speed is controlled through pitch.
2.Horizontal speed is controlled through throttle input.

However, I am having difficulty understanding the specific relationship between throttle input and airspeed. I have theoretical knowledge of Total Energy Control System (TECS), but I need to know how throttle adjustments directly affect airspeed.

Could anyone explain how airspeed is influenced by throttle input? Is there a mathematical relationship or formula that describes this interaction? Any detailed explanation or guidance would be highly appreciated.

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    $\begingroup$ "Could anyone explain how airspeed is influenced by throttle input?" It isn't totally clear what you are asking for. Yes, the primary pitch and power controls you referenced are correct and are taught as good pilot technique - but they aren't isolated from each other: If you maintain altitude and add power you will accelerate. Keep power constant and pitch and your vertical speed changes. There are formulas that I will leave to the aero experts, but the short answer is add power go faster, pull power go slower. Just like in your car. (presuming front side of the power curve) $\endgroup$ Commented Jul 9 at 17:38
  • $\begingroup$ Best to think of the system in an energy-management framework. Pitch and throttle commands work together to effect a change in the state of the system. Not perfect but a helpful reference for this is faa.gov/sites/faa.gov/files/regulations_policies/…. As far as the throttle-to-thrust mapping, of course, that's going to vary widely by airplane and flight condition. $\endgroup$
    – AeroAndy
    Commented Jul 9 at 19:37
  • $\begingroup$ I understand the energy management system handles Total Energy (throttle) and Energy Balance (pitch). However, I can't rely on reference height(also because it keeps changing ) as it doesn't account for terrain altitude. Is there a way to implement the energy management system without considering height, despite its importance? $\endgroup$
    – developer
    Commented Jul 10 at 5:22

2 Answers 2

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If I understand your question and comments, you want a way to get to throttle setting for an air vehicle in prescribed dive conditions (angle, called gamma, and true airspeed). Inherently assumed is zero wind and a trimmed, unaccelerated dive, small angle-of-attack, wings level and no sideslip. Then thrust required will be drag plus weight times the sine of the dive angle:
Tr = D + W*sin(gamma) Remember, gamma is defined negative for a dive. Of course, drag is a function of airspeed and proportional to its square.

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  • $\begingroup$ suppose, I can't use any aerodynamic entities here, since I'm using a simulation and don't have the values of Drag and wight. I have limited accessibility - i.e pitch and airspeed, TECS was something I implemented, however i'm unable to control my airspeed through it @AeroAndy $\endgroup$
    – developer
    Commented yesterday
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You are on the right track: speed is controlled by pitch.

But it is crucial to understand power (throttle) determines whether one climbs, descends, or flies level for a given pitch setting.

pitch controls airspeed, power controls altitude.

No power at all and the aircraft simply glides at the airspeed of the pitch setting. It's (straight line) path is below the horizon.

Gravity is the other factor that can contribute to forward propulsion.

This is how a glider maintains airspeed. Mathematicly, the propulsive force is sine glide angle (to the horizon) × aircraft weight.

To fly with no loss of altitude, add power. To climb, add more. Now thrust is opposed by drag and sine climb angle × aircraft weight.

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  • $\begingroup$ I simulated different conditions to observe how the aircraft will fly at different pitch angles. however I have no information for the weight or drag of the aircraft- since its in simulation (i'm assuming weight as per a model and drag negligible ) I will observe the changes once I implement a propulsive force for the FW in simulation- could you clarify what is he glide angle here ? $\endgroup$
    – developer
    Commented Jul 10 at 5:14
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    $\begingroup$ @developer well, that's what weight and drag are all about. Most of us do well to understand gliding first. Propulsive force = drag at the velocity adequate lift is produced. Propulsive force = sin glide angle × weight. It is important to determine Velocity Best Glide. That's where glide angle (below the horizon) is least. $\endgroup$ Commented Jul 10 at 13:31
  • $\begingroup$ here's what I'm trying to achieve let's assume we have a maximum dive angle , now corresponding to this I want to be able to command an airspeed to descent at a constant air speed i.e (T-D<0) instead of hit and trial to find a throttle percentage to match the dive angle and airspeed. I'm trying to control the throttle as per these conditions. In a simulated world where I let ardupilot give an throttle percentage based on a maximum pitch, this airspeed overshoots $\endgroup$
    – developer
    Commented Jul 12 at 7:20
  • $\begingroup$ I also don't think I can visualize drag here, any suggestions for a better flight simulator (I'm using ardupilot with qcgs) $\endgroup$
    – developer
    Commented Jul 12 at 7:36
  • $\begingroup$ @developer drag will increase from a Vbg minimum both faster and slower. Your maximum glide angle will be based on Vne, or perhaps a bit slower for safety. Using sin glide angle × mass will give exact propulsive force for any glide speed in a linear steady state. Then propulsive force = drag. Note glide angle is also steeper slower than Vbg. This is why Vbg gives maximum gliding distance. $\endgroup$ Commented Jul 12 at 15:17

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