I just watched the video. Now, I understand your question better.
So, the wing loading effect on climb rate is a question derived from comparing two fighters.
Let’s start with drag. There are two kinds of drag: parasitic and induced. The parasitic drag is caused by the movement of air over the whole aircraft. That includes both flying surfaces, like wings, or rudders, and non flying, like fuselage, landing gear, cockpit canopy. Parasitic drag increases with velocity squared. So, simply put, the faster you go, the more parasite drag you get.
The other kind of drag is induced. That is, created by the wing when it makes lift. Think of lift as being energy extracted from the air passing over the wing, so the more lift you make, the higher the induced drag. Induced drag is also higher at higher angles of attack.
In designing a fighter for top speed, you want the parasitic drag to be as low as possible. We will ignore the effects of speed on thrust for the moment. So, in the early days of fighter design, when engine technology was yielding lower power engines than today, Designers gave up wing area to lower the drag and achieve high speed. Airplanes like the F104, or they Mig 21, are examples of this trade off.
If you want an airplane which turns very well, you need to lower the induced drag, and in general, you do this by making a bigger wing, which lowers the angle of attack for a given amount of lift, producing better turn performance.
In comparing the performance of two different fighter aircraft, you have to consider several factors; thrust to weight ratio, wing loading, flight control authority, particularly pitch authority, high lift devices, such as slats and flaps, And all of those must be considered across the speed range in which the aircraft is operating.
High lift devices change the airflow over the wing at high angles of attack. They make the wing more efficient, and create lift at lower speed.
When you actually measure aircraft performance, one of the key factors is specific excess power. That is, the amount of engine thrust available in excess of what is required to maintain 1G flight at that altitude, and that airspeed. So, specific excess thrust comes from engine performance, engine Inlet performance, wing performance, and drag characteristics at that altitude and speed.
Further, when you measure aircraft performance, there is a speed at which the airplane turns with minimum radius, and maximum rate, with no excess thrust available. That speed, which varies with altitude, air density, and aircraft fuel and weapon loading, is known as “corner speed“.
So, back to the video. When the pilots referred to the low wing loading of the F 14, it is really more than that, it is a proxy capturing the airplane’s ability execute a maximum performance turn at either a lower corner speed, or a higher turn rate than the adversary. The F5, for example, has a pretty high wing loading, that is how they get reasonable top speed, with a simple engine in lit, and a relatively simple airframe - They lowered the drag.
But when I take an aircraft like the F5, and I put it in a high G turn, it cannot sustain high G for very long. The induced drag from the small, simple wing is too high, and the airplane slows down, because it does not have the power needed to maintain that G and that turn rate.
When I take an aircraft like the F 14, and I put it in a high G turn, it can sustain the high G, at corner airspeed, because the wing is very efficient. The wing has both large area, and high lift devices that improve performance, which lowers induced drag.
So if both the F5 and the F 14 Begin a turn, the F5 will slow down if it tries to match the same turn rate and radius. The pilot of the F5 must match the turn rate and radius of the F 14, or the F 14 gets behind it. The pilot of the F5 must match the turn rate and radius of the F 14, or the F 14 gets behind it. We used to call it “bleeding” as in bleeding airspeed.
After a turn or two, in which the F5 had to “bleed”, the F14 has the advantage. It is still going fast. Fast enough to transition to a vertical turn, or simply a vertical extension, in which the Pilot unloads the airplane, and does a zoom climb. The F5 is too slow to go into the vertical at that point, so the F 14 out climbs it, gains a position advantage, as well as sufficient separation to employ missiles.
You can think of the turns in the horizontal, but the same tactic: bleed your opponent down, can take place in vertical turns. The fighter with the better turn performance will win the turning fight.
As far as pure climb rate, Yes, with other factors being equal, the lower wing loaded fighter will climb better. But in the video, what they don’t mention, is that the F 14 has lower wing loading, better highlift devices, better acceleration, and better energy addition, which yield better corner as well as climb performance, and those advantages are best exploited in a vertical fight.
The extreme example of low wing loading, would be a glider. But they are terribly slow, and would not make a good fighter. Interestingly, the U2 has incredible climb performance despite mediocre thrust to weight, because of its glider like wing.
All fighter design is a compromise. The compromise with the F 14, was cost. The airframe performance was superlative, but it cost a lot of money to build it.
