Why the heavier the aircraft is, the higher the airspeed must be to obtain the same glide ratio?

I know weight does not affect glide ratio. But why does higher weight need higher gliding speed?

• There are two ways to generate more lift, either fly faster or at higher AoA. Usually a high AoA would reduce your L/D. Aug 12, 2023 at 12:58

In still air, the glide ratio of an aircraft is the same as its L/D ratio (more info here). The L/D ratio of a given aircraft depends only on its angle of attack; a given AoA will always correspond to one particular L/D ratio¹. So if a given AoA could be maintained, the L/D ratio (and thus the glide ratio) would be fixed.

Now, if the weight is increased, the lift required also increases. since we cannot increase the AoA (that would alter the L/D ratio), we must increase the airspeed to obtain the necessary lift.

1 Ignoring the effects of Mach number & Reynolds number

• If AOA is unchangeable, how can I increase the airspeed in a glide? I will have lost my engine and thrust in that situation. Aug 12, 2023 at 15:54
• @Hitomhi -- this is the right answer. I'm converting my explanatory comments, into an answer. Aug 12, 2023 at 17:11
• @Hitomhi for a given glide angle increased weight will increase airspeed. Imagine a car on a hill, one is very light and one is heavily loaded. The heavier one will coast down the hill faster. Aug 13, 2023 at 15:57
• @RobertDiGiovanni: if we ignore the things we usually ignore-air drag, energy going int spinning the wheels, drag because the tire gets flattened where it hits the road, etc. that is not true. Both cars will go down the hill at the same speed. The effect on the glider comes because we need more lift to counter the weight. Aug 13, 2023 at 16:19
• @RossMillikan ah, the feather and the lead ball in a vacuum. This is aerodynamics. An object with the same drag area will fall faster if it is heavier! It's like this: heavier glider --> falls faster --> produces more lift --> which supports its greater weight! This will hold up to significant Mach effects. Aug 13, 2023 at 19:14

The glide ratio depends only on the angle of attack during the gliding descent. Imagine two aircraft in a gliding descent: aircraft A is at its best glide speed, and aircraft B is at the same airspeed and angle of attack as aircraft A, but is heavier.

Since both aircraft have the same airspeed and angle of attack, they have the same lift and drag. In the lighter aircraft, the lift and drag are in equilibrium with the weight, and so the aircraft is in unaccelerated flight- it can keep the same angle of attack all the way to the ground without its airspeed changing.

Since the weight of aircraft B is larger, the forces are not in equilibrium and aircraft B's descent rate. This means a steeper glide path and the change in relative wind means a higher angle of attack if the pitch attitude is not lowered. Aircraft B could raise its angle of attack to arrest the descent rate and keep the same airspeed as aircraft A. But that would negatively affect its glide ratio. If it instead holds its angle of attack the same, it will continue to accelerate until its airspeed is sufficient to arrest the acceleration.

• Both aircrafts have the same lift and drag? B is heavier, isn't the lift of B also higher so as to counteract the higher weight? Aug 12, 2023 at 15:08
• @Hitomhi Lift is a function of only airspeed and angle of attack. Indeed, for unaccelerated flight B needs a bigger lift than A. The only way it can get that lift without raising the angle of attack is to increase its airspeed. Aug 12, 2023 at 15:21
• If AOA is unchangeable, how can I increase the airspeed in a glide? I will have lost my engine and thrust in that situation. Aug 12, 2023 at 15:54
• Re "This means a steeper glide path and the change in relative wind means a higher angle of attack. " -- you are following a mental model where the pitch attitude is forced to remain constant. It is a lot more intuitive to hold angle-of-attack constant. (Because to a first approximation this is what happens when we hold control stick position constant-- or when we just let the glider fly at trim.) Can you generate an explanation of why the heavier aircraft ends up speeding up to a higher airspeed, if angle-of-attack is held constant? It's pretty straightforward... Aug 12, 2023 at 16:48
• @Hitomhi You don't have to do anything increase it. On the contrary, you would have to do something to keep it from increasing. The lift and drag at the lower airspeed are not sufficient to keep you in unaccelerated flight. If you just hold the angle of attack constant your plane can't help but accelerate until the increased drag and lift are enough to stop the acceleration. Aug 13, 2023 at 3:40

In relation to this question, one might ask

"If AOA is unchangeable, how can I increase the airspeed in a glide?"

Let's assume that we are keeping the control stick fixed in the position that corresponds to the best glide angle in steady-state flight. To a close approximation, this means that the Angle-of-Attack (AoA) is fixed. Which-- ignoring Reynolds number and Mach effects-- means that whenever we are in steady-state flight with a fixed control stick position, the glide angle (and glide ratio) is fixed.

If the AoA is fixed, and the airspeed is too low for the present weight and AoA,, then both Lift and Drag will be too low. Meaning specifically that the sum of their components that act parallel to the flight path will be smaller than the component of Weight that acts parallel to the flight path. So the forces acting parallel to the flight path do not add up to zero, so there is a net force acting parallel to the flight path. This force will cause the airspeed to increase.

Meanwhile the forces acting perpendicular to the flight path also do not add up to zero, so the flight path curves earthward, which throws the forces acting parallel to the flight path further out of balance, exacerbating the increase in airspeed.

Eventually everything comes back into balance and the glider is back to the original glide angle at a higher airspeed. The entire process (which I've only described the first part of here) is called a pitch "phugoid". To a first approximation AoA is constant in a phugoid. That's not exactly the case in real life, but if it were, we'd still see an increase in weight lead to an increased glide speed, at the original glide angle. Study the pitch "phugoid" to learn more.

"But why does higher weight need higher gliding speed?"

See above-- that's why a higher weight leads to a higher gliding speed. If you somehow increase the weight of the glider (perhaps by condensing moisture from the atmosphere to add to the on-board water ballast?), while holding the angle-of-attack constant, the airspeed must increase.

• There's another phenomenon very similar to this. When you fix AoA but increase thrust, the airplane will accelerate and have excessive lift, hence fly up, then decelerated by gravity. The end result is a climbing flight, but not faster. Aug 13, 2023 at 2:24
• @quietflyer Do you also mean the speed will increase itself like what Chris says above? Aug 13, 2023 at 5:20
• @Hitomhi Think of a falling feather. Both the glider and the feather have one commonality: both obtain their thrust from their own weight. If you were to increase the weight of the feather, it will have more "thrust", causing it to fall faster. The same is true for the glider. Aug 13, 2023 at 16:35

I know weight does not affect glide ratio

That's correct.

The glide ratio is defined as the ratio (obviously) between the horizontal length flown by the aircraft divided by the relative lost height. Called $$\gamma$$ the relevant angle between these two components, the glide ratio simply equals $$1/\gamma$$:

(Picture source)

To prove this, we simply see from this picture that:

$$D=W sin\gamma$$

$$L=W cos\gamma$$

(Note that in the picture the weight is called $$F_{gravity}$$ while I've used the "standard" letter $$W$$)

If we now write the ratio $$L/D$$ we get:

$$\frac{L}{D}=\frac{W cos\gamma}{W sin\gamma}=\frac{cos\gamma}{sin\gamma} \approx \frac{1}{\gamma}$$

i.e. the ratio $$L/D$$ just equals the glide ratio! Furthermore, the weight $$W$$ has been cancelled out and therefore the glide ratio does not depend on the weight but only on the aerodynamic characteristics of the aircraft.

But if the weight is gone, how comes that

higher weight need higher gliding speed?

That's because when you glide you try to maximize the glide ratio i.e. you try to maximize $$L/D$$. And $$L/D$$ is maximised when you fly at one specific speed which does depend on the weight:

$$V_{L/D_{max}}=K\sqrt{W}$$

where $$K$$ is a constant calculated from $$\rho$$ and the aerodynamic polar of the aircraft and that, in your question, is the same for both the light and the heavy aircraft.

So yes, the glide ratio does not depend on the weight but the speed at which it is maximised does.