Air Craft formula

[Raider5678]

Hey guys, I'm trying to find a formula for the amount of lift a plane will get from it's wings.

 

I'm looking for net lift, as in the entire plane. I realize I have to make sure it's stable, etc.

 

Either way, using the following variables:

 

Wings surface area

Angle of wings

Velocity

 

What formula will tell me how much lift the wings are generating?

 

I've probably got the wrong variables.

Any formula that resembles the solution to this problem helps.

 

 

 

I believe this is it:

https://www.grc.nasa.gov/www/k-12/airplane/lifteq.html

 

But I'm not sure.

Edited July 8, 2017 by Raider5678

[MigL]

Coefficient of lift is empirically derived through wind tunnel testing, originally by NACA, now NASA, but most manufacturers have their own modifications to standard profiles, which are optimized for specific circumstances/missions.

One profile whose Cl is probably in the public domain is the standard 'Clark Y' profile.

( at one time I could have given you the NACA number, I think it was something like be 6xx45 ??? but I don't recall )

[J.C.MacSwell]

Hey guys, I'm trying to find a formula for the amount of lift a plane will get from it's wings.

 

I'm looking for net lift, as in the entire plane. I realize I have to make sure it's stable, etc.

 

Either way, using the following variables:

 

Wings surface area

Angle of wings

Velocity

 

What formula will tell me how much lift the wings are generating?

 

I've probably got the wrong variables.

Any formula that resembles the solution to this problem helps.

 

 

 

I believe this is it:

https://www.grc.nasa.gov/www/k-12/airplane/lifteq.html

 

But I'm not sure.

That's the one. Note that the coefficient will depend on the shape, the angle, and Reynold's number and is generally determined experimentally, so as MigL stated empirically. It increases "fairly" linearly with angle until stall is approached for most profiles, though not zero at zero angle except for symmetric shapes.

[Manticore]

Just do a search (I use Duckduckgo because fuck Google) for aerodynamics software - there's quite a lot.

[studiot]

Hey guys, I'm trying to find a formula for the amount of lift a plane will get from it's wings.

 

I'm looking for net lift, as in the entire plane. I realize I have to make sure it's stable, etc.

 

Either way, using the following variables:

 

Wings surface area

Angle of wings

Velocity

 

What formula will tell me how much lift the wings are generating?

 

I've probably got the wrong variables.

Any formula that resembles the solution to this problem helps.

 

 

 

I believe this is it:

https://www.grc.nasa.gov/www/k-12/airplane/lifteq.html

 

But I'm not sure.

 

 

Unfortunately it's not as simple as that.

Equally too many make it too complicated by long unproductive arguments about the origin of the lift.

So here is an uncomplicated development, accessible to any upper high school pupilof physics / applied maths.

 

 

First let me say that Lift is a vector and it often does not point directly upwards in real flight.

Aircraft climb and descend, bank and turn, and fly at various airspeeds.

 

Initially considering real aircraft shapes and airfoils tends to hide the mechanics of what is going on so I will start with a flat plate.

The plate is inclined to the airstream and we shall see why this is and the effect of that inclination with the help of the figures below.

We shall also see why aircraft like to maintain straight level (horizontal) flight as much as possible.

 

So to Figure1.

 

It doesn't matter whether the air moves over the plate as shown or the plate moves throughstill air, the effect is the same.

In this situation, It is an observed fact that the average pressure pushing down on top of the plate is lower that the average pressure pushing up on the underside.

Typical values are shown for subsonic aircraft. The air pressure above is reduced to about 80% of that below.

 

This difference leads to a normal reaction (at right angles to the plate) as shown in Figure 2.

Since the plate is inclined to the horizontal airflow this reaction is not vertical..

 

The total reaction may be resolved into two mutually perpendicular components, called the Lift and the Drag, as shown in Figure 3.

Now we see the effect of tilting the plate.

The Lift is vertical.

Furthermore we want to maximise the Lift and minimise the Drag.

This happens at low angles of inclination, as shown.

 

So that is straight, level (horizontal) flight.

 

In Figure 4 we turn the vector diagram in Figure 3 round so the air is now rising or the plate descending.

If we maintain the plate to airstream inclination angle, the vectors will be the same but rotated by the angle of descent.

 

So the Lift is no longer vertical.

 

But obviously only the vertical component of the Lift force supports the plate.

 

As we increase the angle of inclination to the airstream, the vectors change, with the Lift reducing and the Drag force increasing as shown in figure 5.

Further the angle of Lift becomes less favourable, but the Drag can be seen to be providing a significant upward contribution.

 

 

 

 

So the developed Lift depends upon how the aircraft is flying.

Furthermore we have only so far discussed straight flight, so the diagrams have been two dimensional.

As soon as we take turning manouveres into account we must resolve the total reaction in three dimensions, not two.

 

 

 

If this is of interest let us know your proposed application for more detail.

 

 

 

[J.C.MacSwell]

 

 

Unfortunately it's not as simple as that.

 

It really is that simple (determination of coefficient aside) if Raider does in fact want lift. How he uses it, and proper application, can be simple or complicated as is pretty much any formula.

[studiot]

It really is that simple (determination of coefficient aside) if Raider does in fact want lift. How he uses it, and proper application, can be simple or complicated as is pretty much any formula.

 

Yes there is a simple formula, but you can't just bung any old numbers into it, as this extract demonstrates.

 

 

 

Some national aeronautical agencies publish tables of aerofoil characteristics to enter into the formula for lift and drag so if you know the wing shape and size you can look up the lift, for various flight conditions.

 

for example

 

Edited July 9, 2017 by studiot

[Raider5678]

 

 

Unfortunately it's not as simple as that.

Equally too many make it too complicated by long unproductive arguments about the origin of the lift.

So here is an uncomplicated development, accessible to any upper high school pupilof physics / applied maths.

 

 

First let me say that Lift is a vector and it often does not point directly upwards in real flight.

Aircraft climb and descend, bank and turn, and fly at various airspeeds.

 

Initially considering real aircraft shapes and airfoils tends to hide the mechanics of what is going on so I will start with a flat plate.

The plate is inclined to the airstream and we shall see why this is and the effect of that inclination with the help of the figures below.

We shall also see why aircraft like to maintain straight level (horizontal) flight as much as possible.

 

So to Figure1.

 

It doesn't matter whether the air moves over the plate as shown or the plate moves throughstill air, the effect is the same.

In this situation, It is an observed fact that the average pressure pushing down on top of the plate is lower that the average pressure pushing up on the underside.

Typical values are shown for subsonic aircraft. The air pressure above is reduced to about 80% of that below.

 

This difference leads to a normal reaction (at right angles to the plate) as shown in Figure 2.

Since the plate is inclined to the horizontal airflow this reaction is not vertical..

 

The total reaction may be resolved into two mutually perpendicular components, called the Lift and the Drag, as shown in Figure 3.

Now we see the effect of tilting the plate.

The Lift is vertical.

Furthermore we want to maximise the Lift and minimise the Drag.

This happens at low angles of inclination, as shown.

 

So that is straight, level (horizontal) flight.

 

In Figure 4 we turn the vector diagram in Figure 3 round so the air is now rising or the plate descending.

If we maintain the plate to airstream inclination angle, the vectors will be the same but rotated by the angle of descent.

 

So the Lift is no longer vertical.

 

But obviously only the vertical component of the Lift force supports the plate.

 

As we increase the angle of inclination to the airstream, the vectors change, with the Lift reducing and the Drag force increasing as shown in figure 5.

Further the angle of Lift becomes less favourable, but the Drag can be seen to be providing a significant upward contribution.

 

 

 

 

So the developed Lift depends upon how the aircraft is flying.

Furthermore we have only so far discussed straight flight, so the diagrams have been two dimensional.

As soon as we take turning manouveres into account we must resolve the total reaction in three dimensions, not two.

 

 

 

If this is of interest let us know your proposed application for more detail.

 

 

 

aircraft1.jpg

Okay.

So ignoring any fancy wing shapes, you want it on an angle, but you don't want that angle to be too high because then there's more drag.

 

 

Just messing around with designing a small model plane, and then a slightly larger one, etc etc etc.

I just wanted to know how to apply some fairly basic aerodynamic formulas to it.

However, this was quite helpful.

[Manticore]

You need to read up on "Reynolds Number". Airfoils suitable for full sized aircraft are not necessarily suitable for small models and vice versa.

 

I suggest you try Martin Hepperle's "JavaFoil" http://www.mh-aerotools.de/airfoils/javafoil.htm and download the UUIC airfoil database http://m-selig.ae.illinois.edu/ads/coord_database.html which contains coordinates for nearly 1,600 airfoils.

[studiot]

Okay.

So ignoring any fancy wing shapes, you want it on an angle, but you don't want that angle to be too high because then there's more drag.

 

 

Just messing around with designing a small model plane, and then a slightly larger one, etc etc etc.

I just wanted to know how to apply some fairly basic aerodynamic formulas to it.

However, this was quite helpful.

 

You need to know more than this for your design.

 

There are four basic forces acting on a plane (plus a fifth I will come to).

 

As shown in the diagram they come in pairs and also generate two couples.

I have shown the conventionally preferable configuration.

 

The 'Lift behind Weight' couple gives the aircraft a tendency to turn nose downwards in the event of an engine failure so it will enter a downward glide.

Lift forward of weight stalls the aircraft's flight.

 

If the drag is above the thrust this counters the first couple to some extent.

 

Both couples can be seen to (preferably) have short lever arms.

 

I have noted a fifth force.

This is developed by the tailplane and can be upwards or downwards and can be changed in flight

As can be seen it has a long lever arm about the CofG of the aircraft.

So a small tailplane can have a large effect.

This effect can be used to counter the rotational imbalance between the other two couples.

It can also be used to boost the vertical lift force at slow speeds (take off and landing) since the lift is speed dependent.

The wingtips in swept back wings can also serve these functions in aircraft without tailplanes.

 

Getting these wrong is the principle reason paper aeroplanes swoop up and stall or drop nose first.

 

 

 

Yes check your dynamic similarity modelling characteristics if you wish to scale down full sized wing shapes, as Manticore says.

The calculations often result in imparactically high airspeed for the model (several thousands of miles per hour).

So some shape adjustment is inevitable.

Edited July 16, 2017 by studiot

[Tub]

May I ask this here: when we hear reports that " ice on the wings " has prevented take-off, is it because the ice adds an incalculable weight-factor to the safe load or is it because the ice alters the shape of the wings so disrupting airflow?

[Area54]

May I ask this here: when we hear reports that " ice on the wings " has prevented take-off, is it because the ice adds an incalculable weight-factor to the safe load or is it because the ice alters the shape of the wings so disrupting airflow?

The ice, as you suspected, alters the aerodynamics of the wing, increasing drag and reducing lift. This can lead to a stall.

 

Some discussion here, but lots of items online: https://www.scientificamerican.com/article/ice-flight-3407/

Edited July 19, 2017 by Area54

[Tub]

Thanks, Area54. Very informative link - sad too, though.

[studiot]

May I ask this here: when we hear reports that " ice on the wings " has prevented take-off, is it because the ice adds an incalculable weight-factor to the safe load or is it because the ice alters the shape of the wings so disrupting airflow?

 

Yes depending upon the thickness of icing both aircraft weight, lift and drag are affected.

This may alter the trim of the aircraft by shifting the four forces mentioned in post#10.

Further effects not so far mentioned are that the icing may seize the flaps, landing gear or disrupt the operation of propellor or turbo aircraft. Jets are not so subject to engine disruption.

 

Here is an interesting breakdown.

 

http://www.pilotfriend.com/safe/safety/icing_conditions.htm

Edited July 19, 2017 by studiot

[Tub]

Thank you, studiot. Fascinating link.