# Using the lift equation, can you make anything fly?

• Quintijn van Heek
The lift equation is an entirely empirical relationship, and ##C_L## actually incorporates a lot of really complex physics. Typically, ##C_L## is determined through some combination of experiments and computations for a specific shape or family of shapes.

#### Quintijn van Heek

If I have a contraption with wings that weighs 120 kg, the wings in total are 2 meter squared, and I make it go 60 km/h, will it fly? According to the lift equation (L = (1/2) d v^2 a CL), it should, since

L=(1/2)*1.225*277.788*2*3.39 = 1176.789
Weight = 120 kg = 1176.789 N
L = lift = 1176.789 N
D = density = 1.225 kg/m^3
V = velocity = 16.667 m/s
V^2 = velocity squared = 277.788 m/s
A = area of wings = 2 m^2
CL = coefficient of lift = 3.39

If my calculations are correct, it should fly, right? Or am I forgetting something? I'm not really sure.

Parth
Quintijn van Heek said:
If I have a contraption with wings that weighs 120 kg, the wings in total are 2 meter squared, and I make it go 60 km/h, will it fly? According to the lift equation (L = (1/2) d v^2 a CL), it should, since

L=(1/2)*1.225*277.788*2*3.39 = 1176.789
Weight = 120 kg = 1176.789 N
L = lift = 1176.789 N
D = density = 1.225 kg/m^3
V = velocity = 16.667 m/s
V^2 = velocity squared = 277.788 m/s
A = area of wings = 2 m^2
CL = coefficient of lift = 3.39

If my calculations are correct, it should fly, right? Or am I forgetting something? I'm not really sure.
Uh, well, sure, as long as you are ok with ignoring major considerations like stability/control, thrust/drag and structural integrity.

...and if you don't mind my asking, how much do you weigh...?

Quintijn van Heek said:
A = area of wings = 2 m^2
CL = coefficient of lift = 3.39

If my calculations are correct, it should fly, right? Or am I forgetting something? I'm not really sure.
I'm not sure but it's quite possible that the area is meant "projection as seen from the front", not the actual size of the wings.
Also the CL looks quite optimistic but possible.
How do you maintain the speed? The drag may be fairly high and should be computed as well.

SlowThinker said:
I'm not sure but it's quite possible that the area is meant "projection as seen from the front"...
It's not; that's for drag.

russ_watters said:
Uh, well, sure, as long as you are ok with ignoring major considerations like stability/control, thrust/drag and structural integrity.

...and if you don't mind my asking, how much do you weigh...?
Thanks. I weigh 55 kg

Quintijn van Heek said:
Thanks. I weigh 55 kg
Not trying to make yourself fly, are you...?

phinds
Quintijn van Heek said:
weighs 120 kg, the wings in total are 2 meter squared, and I make it go 60 km/h, will it fly?
William Devane's character, Major Phil Clark, in Red Flag the Ultimate Game regarding the F-4 Phantom, "You can make a brick fly if you put large enough engines on it," or words to that effect.

Quintijn van Heek and russ_watters
russ_watters said:
Not trying to make yourself fly, are you...?
Well I'm not neccesarily making myself fly, i was just researching the lift equation and I was just wondering wether it waspossible. So then I worked all this out and well now I have an answer :). It was hypothetical though.

Here's some useful information about the lift equation and how some common theories explaining lift are wrong or incomplete:

https://www.grc.nasa.gov/www/K-12/airplane/presar.html

There are several other tracks here for drag, forces and torque and stability.

However, following the track for theories of lift they describe some incorrect theories:

https://www.grc.nasa.gov/www/K-12/airplane/right2.html

https://www.grc.nasa.gov/www/K-12/airplane/wrong1.html

https://www.grc.nasa.gov/www/K-12/airplane/wrong2.html

https://www.grc.nasa.gov/www/K-12/airplane/wrong3.html

https://www.grc.nasa.gov/www/K-12/airplane/bernnew.html

There's also a cool Paper Plane book by John Collins who holds the world record for longest paper plane flight. In the book, he describes the process of building the plane and the work that went into winning the Guinness award:

https://www.amazon.com/dp/1607743884/?tag=pfamazon01-20

and more on John COllins and his paper plane:

bob012345
A lift coefficient of 3.39 is incredibly optimistic. Even with complicated multi-element airfoils, 2-2.5 is more typical as a Cl_max, although 3.4 is definitely possible. It's also worth noting that the drag at this Cl is likely to be quite high. You'd really want either more wing area or a higher speed to make this at all feasible.

Bystander said:
William Devane's character, Major Phil Clark, in Red Flag the Ultimate Game regarding the F-4 Phantom, "You can make a brick fly if you put large enough engines on it," or words to that effect.

A similar statement applies to boats. From a Mercury outboard motor ad in 1964:

I would not want to try that boat on a windy day...

#### Attachments

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jedishrfu, Bystander, russ_watters and 1 other person
Sorry I couldn't resist...

russ_watters, cjl, jedishrfu and 1 other person
Please note that "the lift equation" is an entirely empirical relationship, and ##C_L## actually incorporates a lot of really complex physics. Typically, ##C_L## is determined through some combination of experiments and computations for a specific shape or family of shapes. It's nearly impossible to just look at a random airfoil (or other) shape and guess its ##C_L##.

In principle, you could make any object fly as long as you had enough thrust pointed in the right direction, but it's not always feasible.

bob012345
Bystander said:
William Devane's character, Major Phil Clark, in Red Flag the Ultimate Game regarding the F-4 Phantom, "You can make a brick fly if you put large enough engines on it," or words to that effect.
Indeed. Stunt planes at air shows have engines so powerful they can turn vertical and simply hover. When they turn horizontal, they merely pull themselves through the air.

In fact, because they do so many stunts upside down, their wings are symmetrical in cross-section (cambered top and bottom). The wings aren't needed for lift really, they're needed for stability and maneuvering.

CWatters said:
Sorry I couldn't resist...

WHAT SORCERY IS THIS

DaveC426913 said:
WHAT SORCERY IS THIS
Did someone mention sorcery...

Aww you guys don’t know anything, the ETs have mastered lift best:

jedishrfu
cjl said:
the "handle" is actually vertical and horizontal stabilizers, and the lawnmower deck is a (very stubby, low aspect ratio) wing. Elevons for control are attached to the back of the deck.
Yeah. I saw that. Clever.

[ EDIT ] good lord! It's a kit!

jedishrfu
russ_watters said:
It's not; that's for drag.

Actually the area used in the generic lift, drag relation of 1/2 x density x C x A x V^^2 is arbitrary since the coefficients of lift and drag are by experiment are referenced to the area dimensions selected. A classic text by Prandtl & Tiegens on Applied Hydro & Aerodynamics selected the largest projected area of the wing based on the chord and span for the representative area. Any representative area could be used and the determined coefficient would reflect that selection. Handbook of Fluid Dynamics by Streeter use the airfoil chord as a representative length for a unit wing span. Experimental work I have done required selections for various dimensions be made to determine the complicated unknown coefficients.

You can launch a ballistic missile horizontal from a submarine but why would you want to?
So can pigs fly with JATO.

DaveC426913 said:
Indeed. Stunt planes at air shows have engines so powerful they can turn vertical and simply hover. When they turn horizontal, they merely pull themselves through the air.

In fact, because they do so many stunts upside down, their wings are symmetrical in cross-section (cambered top and bottom). The wings aren't needed for lift really, they're needed for stability and maneuvering.
I think the fact that the engine thrust can match the weight doesn't mean wings aren't needed for level flight. Normal planes can fly upside down also if the angle of attack is still positive but the airfoil isn't as efficient that way.

Quintijn van Heek said:
If I have a contraption with wings that weighs 120 kg, the wings in total are 2 meter squared, and I make it go 60 km/h, will it fly? According to the lift equation (L = (1/2) d v^2 a CL), it should, since

L=(1/2)*1.225*277.788*2*3.39 = 1176.789
Weight = 120 kg = 1176.789 N
L = lift = 1176.789 N
D = density = 1.225 kg/m^3
V = velocity = 16.667 m/s
V^2 = velocity squared = 277.788 m/s
A = area of wings = 2 m^2
CL = coefficient of lift = 3.39

If my calculations are correct, it should fly, right? Or am I forgetting something? I'm not really sure.
I disagree with your calculation assumptions because you can't know what the coefficient of lift is without knowing the design and even then it's very complex as others have pointed out. If your design worked at this speed then it by definition it would have that CL but you can't know that without at least simulations first.

But having said that, yes, in general you could make a small lightweight aircraft that worked at lower speeds. Here is an example;

https://www.wired.com/2012/06/electric-flynano/

You could google WIG planes (wing in ground effect).

Another possibility is to use the Magnus effect for the wings. I say that because theory says you can get very high lift for short wings using this effect. Very roughly, if each wing is a 0.5m diameter rotor one meter long, spinning at 20rev/second, forward motion of the craft moving at 16.67m/s would give lift equal to about your weight plus the 160kg machine if you designed it within the weight parameters. The rotors don't have to be massive or have big moments of inertia either if you design them not to. If your rotors were one meter in diameter, they would only have to spin at 5rev/second or 300 rpm. They don't need to be solid.

My suggestion is get access to a simulation program that does fluid dynamics and test your ideas on the computer to get a feel for how the numbers works out.

zul8tr said:
Actually the area used in the generic lift, drag relation of 1/2 x density x C x A x V^^2 is arbitrary since the coefficients of lift and drag are by experiment are referenced to the area dimensions selected. A classic text by Prandtl & Tiegens on Applied Hydro & Aerodynamics selected the largest projected area of the wing based on the chord and span for the representative area. Any representative area could be used and the determined coefficient would reflect that selection. Handbook of Fluid Dynamics by Streeter use the airfoil chord as a representative length for a unit wing span. Experimental work I have done required selections for various dimensions be made to determine the complicated unknown coefficients.

It isn't really arbitrary, though. You certainly could use the frontal area, for example, and the data would fit, but lift doesn't actually scale with that parameter unless all airfoils have the same ratio of frontal area to planform area. You would end up with relationships that aren't all that general. You are better off using the "correct" area so your relationships collapse onto one another more readily.

There is information available from NASA and other sources on airfoil design where the coefficient of lift has been calculated already for each configuration. Here is one source;

http://airfoiltools.com

Long before such free-flight wonders, control-wire stuff could make you look twice.
IIRC, one aero-modelling magazine even featured plans for a Snoopy(TM) kennel and pilot...