5
$\begingroup$

Consider a glider trimmed to fly at some given angle-of-attack, gliding in smooth air (no thermal convection, ridge lift, wave lift, etc.). If air density is somehow kept exactly constant in all cases, and the glider is launched from the same initial altitude relative to the ground in all cases, would the flight duration be the same in all three cases? (A yes/no question.)

  1. Extra weight has been added to the glider, exactly at the CG, doubling the glider's weight.

  2. We've increased the value of the gravitational constant from 9.8 m/s/s to a higher value (twice as high).

  3. We've caused the earth (and atmosphere) to steadily accelerate straight “up”, at 9.8 m/s/s, thus creating an apparent increase in the gravitational constant (to an apparent value double the actual value). (Acceleration starts well before the glider is launched, not mid-flight. Glider is also accelerating along with everything else at instant of launch, i.e. the atmosphere isn't rushing up past the glider at the instant of launch. For example the glider could launch by rolling off a ramp mounted on a high tower connected to the ground.)

(Edit: to make this more clear, imagine that a giant rocket engine attached to the other side of the earth is causing this acceleration. The earth itself is the only thing that is being directly acted on by the accelerating force; the atmosphere and glider each experience the results of this acceleration in a less direct manner.)

Also, if “yes”, then a second question — launched in equilibrium (exactly at its steady-state trim speed for the existing conditions) from a given height, would the glider stay up for a longer duration or a shorter duration after we've made one of these changes?

The intent of the question is to compare the steady-state in-flight dynamics, not some difference relating to some possible slight variation in the initial kinetic energy imparted at the instant of launch, etc. In each case, the glider is understood to be launched at its steady-state trim speed in relation to the existing conditions.

$\endgroup$
5
$\begingroup$

Scenarios 2 and 3 would be almost exactly the same. Scenario 1 would be very different. However, the glider would be able to stay up for almost exactly the same amount of time in all three scenarios.

The basic summary of what would happen: In scenario 1, both the weight and the mass would be doubled. In scenarios 2 and 3, the weight would be doubled but the mass would remain the same.

The simplest way to distinguish scenario 1 from the others is to pitch into a vertical climb (or a vertical dive). In scenario 1, the glider will accelerate downwards at $1\ g$, but in scenarios 2 and 3, it'll accelerate downwards at $2\ g$.

Scenarios 2 and 3, on the other hand, are almost completely identical. Specifically:

Scenario 2 simply adds more gravity. Pretty straightforward.

Scenario 3 consists of having the ground accelerate "up" at $1\ g$. We can look at this scenario in a frame of reference where the ground remains stationary. In this frame of reference, everything is just like the real world, except that everything is now experiencing an inertial force equal to $1\ g$ straight down.

How does an inertial force work? Inertial forces feel just like gravity. In fact, the only differences between the extra forces in the two scenarios are:

  • In scenario 2, the direction of the extra force changes as you move horizontally, because the direction of "down" changes as you move. In scenario 3, the extra force is in the same direction everywhere: namely, the direction opposite the direction of acceleration.
  • In scenario 2, the extra force gets weaker as you get farther away from the earth. In scenario 3, the extra force is equally strong everywhere.

Both of these differences are probably too small to measure.

Now, finally, I said that the glider will be able to stay up for the same amount of time in all three scenarios. This is because, although the mass of the glider differs between the three scenarios, its weight is the same in all three scenarios. And if the glider is flying at a constant speed in a straight line, weight is the only quantity that matters; mass is now irrelevant, because the glider is not accelerating (in the frame of reference where the earth is stationary).

$\endgroup$
  • $\begingroup$ Hope I didn't change the question on you before you answered; I suspect we were both typing at the same time. $\endgroup$ – quiet flyer Jul 28 at 14:57
  • $\begingroup$ For example the original question said "flight characteristics" which might include some up and down maneuvers but the intent was still to look at the steady-state glide only; the final version is more consistent with that. Good points about the mass difference. Can roll back if needed to something that still references "flight characteristics" or you could mod your answer to still reference the difference in flight characteristics as a point of interest. $\endgroup$ – quiet flyer Jul 28 at 15:00
  • $\begingroup$ Actually I feel your answer is still perfectly fine given the existing state of the question as you explicitly said "Now, finally, I said that the glider will be able to stay up for the same amount of time in all three scenarios. " $\endgroup$ – quiet flyer Jul 28 at 15:02
  • $\begingroup$ Looks like I just forgot which scenario was 2 and which was 3; I'll fix my answer now. $\endgroup$ – Timber Swett Jul 28 at 15:09
  • $\begingroup$ "The simplest way to distinguish scenario 1 from the others is to pitch into a vertical climb (or a vertical dive). In scenario 1, the glider will accelerate downwards at 1 g1 g, but in scenarios 2 and 3, it'll accelerate downwards at 2 g2 g." -- I'm not actually quite sure this is true. I think starting in steady-state flight and then pitching straight down, all three will hit the ground at the same time. Although no longer strictly related to the yes/no question asked, I'd be interested to know if you change your mind on this part after some further reflection. $\endgroup$ – quiet flyer Jul 28 at 15:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.