The Awesome Power of V²

V² (Velocity squared) plays an important part in the equations for many flight-related such as lift, drag, kinetic energy, and dynamic pressure. See how this all plays into factors in soaring we encounter daily.
See how a glider's (or any aircraft's) velocity has a big impact on all of these factors, much more than other factors such as air density, mass, and wing area.
Edit note: At 7:05 I should have written the acceleration formula as ft/sec/sec or ft/sec² (and then wrongly simplifying it to V²). Extra credit for you if you had a little cringe moment with that formula's expression.
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[@ewthmatth]

In the video description you wrote
"At 7:05​ I should have written the acceleration formula as ft/sec/sec before reducing it to ft/sec² or V²."
That's *still* wrong. V² units are ft²/sec². That's not equal to acceleration's units, ft/sec²... The units don't match up.
Just look up the "kinematics equations" of basic physics. You'll see the relationship between velocity and acceleration is a little more complicated. There's no way to "reduce" A to V².
Everything else in the video appears to be correct, though. So I enjoyed watching it. I'm not a pilot but I do remember my basic physics somewhat ;)
Edit: I know the video can't be changed, but the description should be edited to have the right correction. Also, I hope your website doesn't claim A=V².. That would also need to be changed.

[@BillPalmer]

Thanks. I’ve adjusted the comments to better reflect the correct math. Yes, too bad there’s no way to adjust an uploaded video or add on-screen comments.

[@TheSoaringChannel]

Yet another great video Bill! Very well explained.

[@The_Modeling_Underdog]

Great video, Bill. Thanks for sharing.

[@josephconleith9606]

Nice one ! Thanks from Switzerland.

[@tonymottram1396]

I really enjoyed the video

[@PureGlide]

Wow look at that street/convergence at the end! Epic.
Good video thank you, made me think about how much harder it is for us in New Zealand below 4000 feet in the thick dense air most of the time...

[@BillPalmer]

Isn’t it a beauty? Here in Southern California we’re often in the blue but occasionally get these nice convergence streets

[@danAtUtah]

Thanks for making this video! If we replace the glider and IAS with a car and speedometer reading, I have a few folks who could benefit from understanding how their driving habits contain dangerously more energy...
Also, small 🤓moment, but doesn't the V^2 term cause polynomial growth of energy, not exponential (r^V)?
Keep it up! wonderful editing in your films.

[@BillPalmer]

Fair point. But for the layman “exponential” is used to differentiate it from “linear.” If I said “polynomial” eyes would glaze over in most viewers. (The ² is an exponent at least)

[@RJLM330]

Thanks BILL

[@BillPalmer]

Hey Bob! Long time no see 😁

[@RJLM330]

@@BillPalmer yep 5years 1month 12 days to be exact. Let’s catch up offline some how.

[@victorbutry]

Why at 7:07 "A=ft/sec * ft/sec"? A = ft/sec/sec!

[@BillPalmer]

That would have been a better way to write it. The product is still m/s^2

[@philatkin7358]

@@BillPalmer No. Velocity squared is not the same as acceleration, which is why the units are different. Also, there is no relationship between velocity and force. Your video is very clearly expressed - thank you - but unfortunately in this respect your analysis is incorrect.

[@BillPalmer]

@@philatkin7358 well there’s a clear relationship between the lift and drag forces and velocity.
Also the force required to stop (in the same distance) - the KE you need to dissipate - has that ^2 relationship with velocity - which was the point.

[@philatkin7358]

@Bill Palmer My second sentence wasn’t very precise - apologies. What I meant was that for a given mass there is a relationship between the force on it, and its acceleration (F=ma, as you said). There is no such relationship between the force and the velocity, nor velocity squared. Velocity squared is not the same as acceleration! Its units are m^2/s^2 (c.f. m/s^2). At the start of a winch launch your acceleration is very high (large force on the glider from the cable) but your velocity is near zero (and so is the square of your velocity). Your statements about lift, drag and KE are absolutely correct.