The Lift Equation - Part 2

Welcome back to Helicopter Lessons in 10 Minutes or Less!

The next element in the Lift Equation deals with air density using 1/2p (Greek symbol for "rho"). At this point I note that math buffs may see the "1/2" and say this doesn't necessarily have to be here in the formula and could technically be put anywhere else in the equation while still making sense. You're right. But I'll get in to it later about why this is normally found at this point in the equation. Back to the topic, Rho covers density. Density is the measure of the thickness or viscosity of a substance. For Helicopters specifically, air density affects how easily the rotor can move the air molecules around it. For helicopters, more air density = better performance. Denser air is simply easier to move. The blades grip and push the air better. Let's cover what makes air denser.
1. Atmospheric Pressure: higher pressure means there are more molecules in 1 given area. This fluctuates day by day and region by region. Higher pressure increases air density and increases performance.
2. Altitude: as altitude increases, the air is thinner because molecules are spaced farther apart. Lower altitude increases air density.
3. Temperature: warm air expands and moves farther apart which decreases air density. Low temperatures increase air density.
4. Moisture: water vapor weighs less than dry air and displaces it. As moisture increases air density decreases. Lower moisture content increases density.
Summary: High Pressure, Low Altitude, Low Temperature, and Low Moisture increase air density and therefore improve performance.

The last element in the equation is by far from most important. This part is Velocity Squared. This is the relative velocity of the air over the airfoil. As I mentioned in other videos this can affect lift more drastically than any other variable because it affects exponentially. If speed over the airfoil doubles, lift quadruples. If speed is halved, lift is quartered. This loss of air velocity could even affect the Coefficient of Lift by causing a stall condition due to the Angle of Attack in the blade now exceeding the critical angle. The loss of air velocity could cause a reduction in surface area as well if rotor RPM is allowed to slow enough for coning to occur.

The last part I wanted to address is that the part of the formula 1/2p X V squared" is actually the measure of Dynamic Pressure. This is the same formula used to calculate airspeed in your pitot tubes. Some references even cite the Lift Equation as using Coefficient of Lift times Surface Area times Dynamic Pressure.

The biggest takeaways from this formula is that each variable can increase or decrease lift and that Velocity Squared has the greatest impact. That wraps up part 2 of 2 if the Lift Equation. Thanks for watching! Don't forget to hit like and subscribe below. As always, safe flying!

If you enjoyed the video or have any questions or comments, hit the like button and comment below.

[Scott.Farkus]

Hey man, I like your videos on helicopters. Could you do some on helicopter flight maneuvers, flight patterns, advanced maneuvers like R2T turns a walk through of how to do those type of maneuvers?

[lple]

Interesting, living in the UK I always associate high pressure with higher temperatures. Need to look into this next I think. Thank you.

[everardoarredondo]

Thanks for all the videos. I have used your videos during my training and have been transitioning to the AStar. There is little information on the difference between power on Vne and power off Vne and why they are different. Could you do something on that. Thanks

[sahjadkhan]

Hi Jacob, it was really informative. I am working on rc engine powered helicopter. Can you please make a video on how to do the thrust calculations of helicopter and what dimensions should be of main and tail rotor? What dimension and thrust ratio should be between main and tail rotor?
Please if you give some clarification on it, that will be very helpful for me.
Thank you.

[Littlewings]

This is great thanks a lot bro❤️❤️❤️❤️

[davidwallace]

I would like to see a real world application of the formula as used in flight planning. Thanks again for your efforts.

[vinnynguyen]

Hi there, great videos. I wonder what velocity to consider here because the velocity is different at every point on the blade? For the sake of calculation, should we use the mid-point of the blade?
Thanks

[kandyfleming]

Great explanation of the lift equation. Thank you!

[jakubgaaska]

How does the number of blades affect the lift? No matter the amount the surface are of disc remains the same as well as the speed, is it just the matter of maniuplating center of weight?

[Captainziadkhan]

Velocity square but how to calculate it for rotating blade ? V= r*w(omega) but what is r ? Half dia ? But that’s going to be just tip velocity ?

[karlfriedrich]

Thanks for such a good explanation of the variables! To be clear, this is only for a single blade, correct? In a 3 blade system you would assume (roughly) slightly less than triple the resultant force?

[Practicaltrain]

I love it(by son of the users) ! Well explained!

[muttnjeff]

Hi Jacob, Your programs are excellent! I flew helicopters for the Navy and Army for 8 years.
How can lift vary by velocity squared at air speeds beyond translational lift? In other words, how can lift increase velocity squared from 30 knots to 40 knots? What have I missed here?

[iandavison]

That explanation helps a lot in understanding lift. But does it not imply that at zero velocity (= hover) there is no lift?

[ftmhaidar]

Hi, thanks for your useful videos . Ive a question, how do you know how much weight is required to make the right amount of lift to avoid it from unstable flight?

[Scott.Farkus]

So we know that some rotor systems have better performance than others; are more efficient rotor systems less susceptible to VRS?

[PennsylvaniaPanda]

I know this is late but what measurements do you use? mm, cm, or inches. Km or Miles.

[mikkopousi]

How does the equation take the rpm of rotor blades into consideration? Since that also matters to the amount of lift generated. Rigth?

[bencrawshaw]

I still don't get how you can come up with a number for lift coefficient. Do you use the angle of attack or the angle of incidence. Sorry I'm slow

[paulrun]

What would the velocity be durring take off? Your not moving so wouldn't the velocity be zero. How would you use this equation to consider a helicopter getting off of the ground ?