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I am currently trying to create a basic flight simulator and am very confused by the concept of lift. This is the equation of lift shown below that I found on the internet. $$ F_l = \frac{1}{2} \rho v^2 C_l A $$ It seems like the lift force would very quickly increase with airspeed (velocity). What I am unsure about is, what forces counteract lift to prevent it from reaching an extremely high value.

For other forces such as thrust in a plane, there tends to be a maximum force applied, so an opposing force such as drag cannot exceed it. But for lift, there doesn't seem to be one.

As the force of lift increases, won't it increase the velocity as a result, and through this increase in velocity, increase the force of lift and so on, until an extremely high value is reached? Of course, this will never happen in real life.

So what factors am I forgetting to account for that prevent this from happening?

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    $\begingroup$ How would an increase in lift increase velocity? $\endgroup$
    – marlonwood
    Aug 25, 2023 at 8:58
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    $\begingroup$ "As the force of lift increases, won't it increase the velocity as a result" -- why? If I'm cruising level at 100 knots and I pull back the stick to start a loop, does my velocity start increasing? What if I have a bunch of extra power in reserve and I open the throttle to exactly offset all the extra drag from the increased angle-of-attack -- in that case does the airspeed start increasing as the flight path curves upward, even though the weight vector is gaining a component that acts opposite to the direction of the flight path? This question doesn't make sense. $\endgroup$ Aug 25, 2023 at 10:39
  • $\begingroup$ If you roll 90 degrees and pull the stick all Lift goes into the turn. But the drag profile of the aircraft in the direction of excess lift is much, much greater than head-on. The longitudinal stability of the aircraft will try to point it in the direction of the new relative wind, ie, the turn. $\endgroup$ Aug 26, 2023 at 18:06
  • $\begingroup$ Note that by definition, Fl is always perpendicular to v. If the airplane does gain some upwards velocity as result of lift, the airflow direction also changes. $\endgroup$
    – jpa
    Aug 27, 2023 at 9:32

8 Answers 8

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It seems like the lift force would very quickly increase with airspeed (velocity). What I am unsure about is, what forces counteract lift to prevent it from reaching an extremely high value.

Let's look at your equation -

$$ F_l = \frac{1}{2} \rho v^2 C_l A $$

and lets rearrange to isolate the unknown variable -

$$ \frac{2F_l}{\rho v^2 A} = C_l $$

Now let's discuss. In level flight, $F_l$ is a constant equal to the known weight of the aircraft. And we know $\rho$ is a constant. The variable $A$, which is dependent on the aircraft, is also a constant. But look... $v^2$ is there on the bottom and when $v$ gets larger, $C_l$ has to get smaller. And why is that? When the aircraft is in level flight, the force of lift $F_l$ - in other words, the weight - doesn't change. Consequently, only the velocity, and the lift coefficient, which is dependent on velocity, change. This is only true, tho, in level flight, for something called the static performance condition of the aircraft. Increase the velocity, and the coefficient of lift will decrease in proportion to the square of the velocity. But the lift will remain the same.

Ok... So what changes the lift coefficient? As flight velocity increases, to keep lift the same, the angle of attack of the wing must be decreased. Since the coefficient of lift is proportional to the angle of attack, a decrease in the angle of attack will proportionally decrease the coefficient of lift.

So the lift coefficient is also dependent on the angle of attack of the wing! That is why maneuvers with the aircraft are limited to velocities and force loadings within the performance envelope defined by the v-n diagram for that aircraft. If the angle of attack is abruptly increased, the lift coefficient is abruptly increased, and the consequent increase in lift can exceed the load-bearing limit of the wing. Nevertheless, more gradual increases in the lift coefficient can occur in level flight when the aircraft is banked. Even tho the flight path may remain level and $v$ may remain constant, the increase in wing loading is inversely proportional to the cosine of the angle of bank, meaning that in level flight, as the bank angle increases, the wing loading increases. Why is that? The effective weight of the aircraft has increased in direct proportion to the inverse of the cosine of the angle of bank. Consequently, the angle of attack of the wing must be increased in response. What increased the effective weight of the aircraft? Well, centrifugal force, of course. The flight path of the aircraft, even tho level, is a circular arc. The centrifugal force is the horizontal component of the lift force produced in the bank. The vertical component is still equal to the weight of the aircraft. This answer may provide other insights.

So... everything is cool. It's not seemingly complicated. We just need to understand what changes in the equation, and why.

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What I am unsure about is, what forces counteract lift to prevent it from reaching an extremely high value

The airplane disintegrating is what would stop aerodynamic forces to grow too much.

That's why any aircraft has well defined speed limitations which must not be overcome. For example one of these speed limitations is called, quite meaningfully, "never exceed velocity".


This is the equation of lift: $F_l = \frac{1}{2} \rho v^2 C_l A$ It seems like the lift force would very quickly increase with airspeed (velocity).

In that equation (which is correct) there are four terms, two of which can become zero more or less independently i.e. $v$ and $C_l$. So if $C_l$ is zero then the speed can become as big as possible but the aerodynamic force would remain anyway null.


I am currently trying to create a basic flight simulator and am very confused by the concept of lift.

Sorry but that sounds like "I'm building a vehicle and I'm very confused by the concept of wheel" 😉

I'd suggest you to read some basic books about airplanes like Raymer's "Simplified Aircraft Design for Homebuilders". This NASA beginners guide to aerodynamics might also be helpful.

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It seems like the lift force would very quickly increase with airspeed (velocity).

That's right, provided that angle-of-attack stays constant.

As the force of lift increases, won't it increase the velocity as a result

Why?

You have some confusion about basic physics. The lift vector acts orthogonal (perpendicular) to the flight path and thus has no tendency to drive an increase in airspeed, generally speaking.

There are situations where the lift vector has an indirect tendency to drive an increase in airspeed. One such situation is during the third quarter of a loop, starting from the point where we are exactly inverted. The lift vector acts earthward and so at that instant, both the lift vector and the gravity vector are acting perpendicular to the flight path, curving (bending) the flight path earthward (downward). As the flight path curves earthward, the gravity vector gains a stronger and stronger component acting parallel to the direction of the flight path, driving a rapid increase in airspeed, even in a glider where thrust is zero.

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It seems like the lift force would very quickly increase with airspeed (velocity). What I am unsure about is, what forces counteract lift to prevent it from reaching an extremely high value.

It's the other way around: lift is used to counteract the force of gravity. To increase lift, you increase speed, angle of attack (AoA) or both. It is true that lift increases dramatically with speed, read further for more about that.

For other forces such as thrust in a plane, there tends to be a maximum force applied, so an opposing force such as drag cannot exceed it. But for lift, there doesn't seem to be one.

Drag certainly can and will exceed thrust. That is how airplames slow down. As stated above, the opposing force to lift is gravity. There is a limiting factor to lift, it is the critical AoA of the wing above which lift diminishes dramatically, and structural strength of the wings.

As the force of lift increases, won't it increase the velocity as a result, and through this increase in velocity, increase the force of lift and so on, until an extremely high value is reached? Of course, this will never happen in real life.

Again, it's the other way around. To increase lift, you increase speed, AoA or both. Speed is controlled by throttle, limiting factor being drag, and AoA is controlled by elevator, limiting factors being critical AoA and structural loads.

P.S. let's not drag how gravity is not a force into this😃

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There are actually 2 opposing forces to lift: gravity (directly) and drag (indirectly).

Drag limits the speed one can go, thereby limiting the v$^2$ factor.

But if lift does exceed weight, flight path turns upwards. Since the engine/prop is less efficient at producing vertical force than the wing, again speed is limited. The thrust force must increasingly oppose the drag and weight, decreasing velocity.

One can see, in a vertical climb, the wing is useless.

Structural strength of the plane, G load limit, also limits amount of lift applied. So, one can go into a high speed dive and apply maximum lift, only to have the wing spar fail.

And, of course, there are human pilot G load limits.

In the end, it is thrust performance and low drag that is desired, with just enough wing lift to carry the load.

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Nothing forces it from increasing quickly. At high airspeeds an airplane cruises with a small angle of attack to reduce its lift. If it suddenly increases the angle of attack its lift will go up dramatically. This can cause the airplane to break apart mid-air.

You have some misconceptions about acceleration and velocity. Lift is always perpendicular to the airplane's flight path and so doesn't increase or decrease its speed- it causes the flight path to curve upward or downward.

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Possibly the most useful single concept to understand is that of energy; the engine adds energy and it’s lost in parasitic and induced drag, anything remaining may ge converted to kinetic energy or potential energy. To address your question directly, lift always has a component that’s in the opposite direction to thrust, so will always tend to slow the aircraft rather than speed it up.

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    $\begingroup$ "lift always has a component that’s in the opposite direction to thrust" -- why? $\endgroup$ Aug 25, 2023 at 10:40
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    $\begingroup$ @Frog If you're taking about induced drag, that is not a component of lift. Lift is defined as the component of the net aerodynamic force which acts perpendicular to the flight path vector. Therefore, by definition, lift does not have a component opposite to thrust (assuming thrust acts in the direction of flight). $\endgroup$ Aug 25, 2023 at 10:44
  • $\begingroup$ @quiet flyer - you’re right, it’s not invariably the case, but the OP seems worried that lift can somehow increase overall speed, which suggests that lift has a component in the same direction as thrust, although I doubt that they have considered the problem in quite those terms. $\endgroup$
    – Frog
    Aug 25, 2023 at 20:18
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At its crudest, there are four forces in play that your simulator needs to deal with. Thrust, drag, lift, and gravity. And they all act on different parts of the aircraft. An imbalance arising from changing any of those forces results in a change in the velocity of the aircraft to reestablish balance, so yes, lift increases with forward velocity, but forward velocity is a consequence of balancing thrust and drag and since drag is not linear, high velocities are only possible with massive thrust, and with massive thrust, you can rocket to the moon.

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