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On its 59th flight, Ingenuity achieved a height of 20 meters - twice as high as its maximum height during the original 5 flights that it was designed and expected to last for. In the scheduled 61st flight, the plan is for it to climb 24 meters.

It seems reasonable that they will continue pushing these boundaries as long as Ingenuity lasts. How high could it climb?

I would assume that it is limited by:

  1. The time/power it takes to ascend
  2. Different air properties, such as lower pressure, at higher altitudes
  3. Software not being able to handle the ground being so far away (this has been the case in the past for Ingenuity, requiring a software upgrade to go past 15 meters)

Which of these reasons, or others, would ultimately limit the helicopter? And at roughly what height would this limit take effect?

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  • $\begingroup$ Isn't "how high can Ingenuity fly" what they're trying to determine with this series of experiments? $\endgroup$ Commented Oct 2, 2023 at 16:25
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    $\begingroup$ Yes, but I do not feel as if that makes the question invalid - there is surely some upper limit that can be estimated beforehand. $\endgroup$
    – BaileyA
    Commented Oct 2, 2023 at 16:44
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    $\begingroup$ On paper spec the alt was 33ft, but in subsequent flights on mars theyve managed almost 66ft $\endgroup$ Commented Oct 2, 2023 at 16:53
  • $\begingroup$ The answer provided is predicated on safe landing on available battery power. What if this limit were removed and the question becomes about absolute aerodynamics performance envelope? At 100% power how high could it go before it would just stop going up? $\endgroup$
    – BradV
    Commented Oct 3, 2023 at 14:29

1 Answer 1

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While Ingenuity would theoretically eventually hit a "service ceiling" above which the atmosphere is no longer dense enough to provided a TWR (Thrust-Weight-Ratio) of above 1, I suspect the major limit is Ingenuity's battery life/flight endurance.

According to the specifications from Wikipedia, the critical numbers are:

Maximum range, radio: 1000m

Flight time: Up to 167 seconds per flight

Maximum possible speed: Vertical: 3 m/s

So, disregarding acceleration and assuming that the flight profile is a straight ascent followed by a (controlled) descent, you would be able to budget 83.5 seconds to ascending which would reach a height of around 250 meters (double that if a crash-landing is acceptable).

To validate that atmospheric pressure reduction with altitude plays no significant role at this scale, the following formula can be used:

Barometric formula for pressure at height h:

$$P(h) = P_0 \times \left(1 - \frac{L \times h}{T_0}\right)^{\frac{g \times M}{R \times L}}$$

Variables:

  • $P(h)$ is the pressure at height h
  • $P0$ is the pressure at sea level (or surface level in the case of Mars)
  • $L$ is the temperature lapse rate
  • $h$is the height above sea level
  • $T0$ is the temperature at sea level
  • $g$ is the acceleration due to gravity
  • $M$ is the molar mass of the planet's air
  • $R$ is the universal gas constant

Constants for Mars:

  • $P0$ = 640 Pa (Pressure at surface)
  • $L$ = -0.0045 K/m (Temperature lapse rate)
  • $T0$ = 210 K (Temperature at surface)
  • $g$ = 3.72076 m/s^2 (Acceleration due to gravity)
  • $M$ = 0.04334 kg/mol (Molar mass of Mars' air)
  • $R$ = 8.314 J/(mol·K) (Universal gas constant)

Evaluating for our 250-meter flight, we get about a 2% drop in pressure, which is negligible.

As for software, while I don't know exactly what Ingenuity runs, I don't see a reason why it couldn't be modified to enable flight to much higher altitudes. Yes, it relies on optical flow (camera sees ground) to stabilize, but (as someone who has experience building and flying drones), there shouldn't be any reason why an IMU-only approach couldn't be used if it is so high that the camera can no longer properly see the ground (although it would probably not land in exactly the same spot as where it took off).

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    $\begingroup$ This is comprehensive and convincing! Thanks :) $\endgroup$
    – BaileyA
    Commented Oct 2, 2023 at 17:11
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    $\begingroup$ could rotor auto-rotation be used for an unpowered descent for most of downward travel in order to conserve battery for final landing? $\endgroup$
    – BradV
    Commented Oct 2, 2023 at 19:43
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    $\begingroup$ "you would be able to budget 83.5 seconds to ascending" – Well, technically, the question didn't require that the aircraft land intact … $\endgroup$ Commented Oct 2, 2023 at 20:53
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    $\begingroup$ @JörgWMittag I.e. "How high could Ingenuity's last flight be?" $\endgroup$
    – Barmar
    Commented Oct 3, 2023 at 14:48
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    $\begingroup$ @BradV Autorotation? Maybe, but I'm skeptical. Ingenuity's props are very unlike traditional heli props being very lightweight and having much less inertia. They're also a significant fraction of the whole drone's mass and need to spin very quickly to lift in the thin atmo. Maybe an absolutely last second "flare" could make the landing survivable, but again, I'm skeptical. $\endgroup$
    – Dragongeek
    Commented Oct 3, 2023 at 19:30

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