Engineering Paradox: Weight & Thrust/Weight

In summary, the two apparently true statements for airplanes in flight are: 1) Lift must equal the weight of the airplane (based on Newton's 2nd Law of motion - Lift = Weight), and 2) Commercial airliners such as Boeing 747-400 and Airbus 320 have thrust-to-weight ratios of about 0.3. However, a paradox arises when applying these equations to the B-747 - it should be impossible for the airplane to fly, but it does in practice. One of the equations (a) and (b) is false, but which one is false is unknown.
  • #1
Biggles 1984
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TL;DR Summary
Aero engineers are confronted with two apparently true but contradictory statements for airplanes in flight:
a) Lift = Weight; and
b) Thrust / Weight = 0.3

The example of a Boeing 747 is used to show that these two equations are incompatible. Both cannot be true. But which one is false?
Engineers are confronted with two apparently true but contradictory statements for airplanes in flight:

a) Lift must equal the weight of the airplane (Lift = Weight), based on Newtons 2nd Law of motion (i.e. Force = ma); where gravity is used to calculate weight (i.e. Weight = mass x gravity).

b) Commercial airliners such as Boeing 747-400 and Airbus 320 have thrust-to-weight ratios of about 0.3.

A thrust-to-weight ratio is a standard engineering term that is defined as the maximum engine thrust (in Newton force), divided by the maximum take-off weight (MTOW), also in Newtons.

thrust-to-weight = Max. Engine Thrust / MTOW

These two equations (a) and (b) are combined to provide equation (c), as follows: If ‘Lift = Weight’ (a) was true; then airliners’ that fly with thrust-to-WEIGHT ratios of 0.3 (b); logically must also fly with thrust-to-LIFT ratios of 0.3 (c); This is summarised by the equations:

(a) Lift = Weight
(b) Thrust / Weight = 0.3
(c) Thrust / Lift = 0.3

For example, Boeing 747-400 (B-747) specifications:

- A maximum mass of 396,890 kg provides a weight of 3,890 kN (i.e. 3,890 kN = 396,890 kg x 9.8 m/s2).

- Four Pratt & Whitney PW4062 engines each with a thrust of 281.6 kN provide a maximum total engine thrust of 1,126 kN (i.e. 1,126 kN = 4 x 281.6 kN).

- Aircraft thrust-to-weight ratio of 0.3 (i.e. 0.3 = 1,126 kN / 3,890 kN).

Thrust to Weight ratios.png


Image: B-747, Thrust / Weight = 0.3

But there is a problem. Applying these equations to the B-747 produces a result that is implausible. See image attached.

- It should be impossible for the B-747 to fly, as the lift required exceeds engine thrust by a wide margin of 2,764 kN. The B-747 would not even be able to take-off with engine thrust of only 30% of the lift required to fly. Yet the B-747 flies in practice.

- There is no plausible explanation how a B-747’s wings can produce lift 245%, or 2,764 kN, in excess of thrust. Lift cannot be created from nothing, and the engines are the only mechanism pushing the airplane forwards and up. Therefore, engine thrust must be greater than lift (i.e. Thrust > Lift). Not vice versa. Observations from airplanes in flight confirm this assertion. The backwash from engine thrust far exceeds the downwash from wings created due to lift, by a wide margin.

This analysis means that equation (c) ‘Thrust / Lift = 0.3’ is false. Hence a paradox arises, as both equations (a) and (b) appear to be true when stated individually, but when combined produce a result, equation (c), that is false (i.e. impossible).

Thrust to Weight ratio - 2.png


Therefore, one of the equations (a) and (b) is also false, but which one?
(a) Lift = Weight
(b) Thrust / Weight = 0.3

Sources for data: www.boeing.com and https://modernairliners.com/boeing-747-jumbo/boeing-747-specs/
 
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  • #2
Very few airplanes have enough thrust to lift an airplane straight up. The few that do are military planes. It is true that lift must equal weight for a plane to fly straight and level. But that does not require so much thrust. With no thrust, an airplane is a glider and will sink to the ground at a certain speed. It only requires enough thrust to make it fly level instead of sinking like a glider. It is sort of like the thrust is lifting the airplane on an inclined plane provided by the wing and the aerodynamics rather than straight up.
 
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  • #3
Most airplanes can fly in level flight at thrust to weight ratios of 0.07 to 0.10. They need more thrust to fly faster, to climb, and to accelerate to take off.
 
  • #4
So how can lift be 10x the engine thrust? Where does the extra lift to fly come ?
 
  • #5
Planes need more thrust to fly faster and slower. The maximum provided thrust to weight ratio is much higher than what is required for cruise flight.

You're simply comparing apples to oranges.
 
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  • #6
The wings. The wings make the plane go up, the engines make the wings go forward
 
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  • #7
The glide ratio of a 747 is 17:1. So the thrust required for it to fly level is only about (very roughly) 1/17th of its weight. So at 1/10th, it has spare thrust for climbing and maneuvering.
 
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  • #8
Welcome, Biggles 1984! :cool:

For level flight at crusing speed, the thrust from the engine(s) is only necessary to overcome the total drag, which is formed by the parasitic and the lift-induced drags.

Please, see:
https://en.m.wikipedia.org/wiki/Lift-to-drag_ratio

What the wing does with that thrust force to convert it to lift force is another matter.
With the excuse of any purist, you could compare what a wing does in that regard with what a gear box does with input and output torques.
Like with the gear box, for the magic of the wing, you need to consider velocities besides forces or torques alone.

For example, this man-powered airplane could fly a total weight of 795 N using only a propeller thrust of 27.5 N:
https://en.m.wikipedia.org/wiki/PSU_Zephyrus

On the other end of the spectrum, any aerobatic airplane that can hover in vertical position while hanging from the propeller has a lift-to-drag ratio of one or greater.

More thrust seems to be a good idea, but that has a costly penalty in weight and fuel consumption.

ldmax_curve.jpg
 
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  • #9
Biggles 1984 said:
So how can lift be 10x the engine thrust? Where does the extra lift to fly come ?
What's the difference between these two flying things in terms of lift and thrust?
1608222057159.png
1608222138192.png
 
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  • #10
Work is force times distance. Counter-acting a glide ratio of 17:1 only requires 1/17th of the force because the distance is 17 times as great. Again, very rough estimates, but it illustrates the point.
 
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  • #11
Actually, this is simple, but much worse than I thought:
Biggles 1984 said:
But there is a problem. Applying these equations to the B-747 produces a result that is implausible. See image attached.

- It should be impossible for the B-747 to fly, as the lift required exceeds engine thrust by a wide margin of 2,764 kN. The B-747 would not even be able to take-off with engine thrust of only 30% of the lift required to fly. Yet the B-747 flies in practice.
You're simply declaring the reality to be "implausible". You simply don't believe that the lift can be much larger than the thrust -- well, ok, you're wrong. And you've created an equation, that you don't explicitly state, is what you believe:
d. Lift = thrust

That's the equation that is wrong.
 
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  • #12
I'm saying that the lift produced by the wings cannot exceed engine thrust.
 
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  • #13
Biggles 1984 said:
I'm saying that the lift produced by the wings cannot exceed engine thrust.
Understood: that's wrong.
 
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  • #14
but then where does the lift come from?
 
  • #15
Biggles 1984 said:
but then where does the lift come from?
The wings.
 
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  • #16
Biggles 1984 said:
I'm saying that the lift produced by the wings cannot exceed engine thrust.
Think of the situation, in terms of work and energy transfer in ideal conditions (no parasitic drag), like a simple machine and its ideal mechanical advantage: the incline.

http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/incline.html#c1

For certain horizontal distance, the airplane tends to fall certain height (think of a glider).
The work done by the thrust force along that certain horizontal distance translates into work done by the lift force up that certain height or vertical distance.
When everything is in balance, level flight can be sustained... until you run out of fuel.

Again, what you seem to be missing is how much mass of air and at what velocity each, engine and wing, constantly moves.

Please, see:
https://www.grc.nasa.gov/www/k-12/airplane/ldrat.html
ldrat.gif
 
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  • #17
Are you saying that the wing produce almost 2.5x as much upward force than the maximum engine thrust (which is used to push the airplane forwards and up)?

That's not possible because it breaches the physics principles of conservation of energy, momentum and force. Wings cannot create a force from nothing.
 
  • #18
Biggles 1984 said:
Are you saying that the wing produce almost 2.5x as much upward force than the maximum engine thrust (which is used to push the airplane forwards and up)?

That's not possible because it breaches the physics principles of conservation of energy, momentum and force. Wings cannot create a force from nothing.
Forces do not need to be equal; there is no such thing as "conservation of force". And force is neither energy, nor is it momentum. The ramp example was a good one. So is a wedge. So is a pulley system.

Look; planes fly. You believe they fly, don't you? You should accept that reality at face value and try to learn why rather than just saying you don't believe it should be possible.
 
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  • #19
Biggles 1984 said:
Are you saying that the wing produce almost 2.5x as much upward force than the maximum engine thrust (which is used to push the airplane forwards and up)?

That's not possible because it breaches the physics principles of conservation of energy, momentum and force. Wings cannot create a force from nothing.
In the following real life diagrams, what force is always greater, L or D?

For level flight:
L = Weight
D = Thrust

I03xP.png
 
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  • #20
That is the argument that I heard from engineers as well, and it's a logical fallacy. It's not science.
 
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  • #21
In contrast. If you can agree that the backwash from engines is greater than the downwash from the wings. Then it follows that the thrust form the engines is greater that the lift produced by the wings.
 
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  • #22
Biggles 1984 said:
That is the argument that I heard from engineers as well, and it's a logical fallacy. It's not science.
We are engineers and scientists. And at this point, I don't think you are interested in learning. You're saying things that are obviously false, stating scientific laws incorrectly - even inventing ones that don't exist. Ultimately the choice is yours whether you want to learn or not, but we don't have to humor your effort.
 
  • #23
Biggles 1984 said:
In contrast. If you can agree that the backwash from engines is greater than the downwash from the wings.
It's not.
 
  • #24
This thread is clearly not going to become productive and is therefore locked.
 
  • #25
Anybody else notice the irony in his avatar choice? Maybe doghouses can fly better without wings? o0)

1608224655273.png
 
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  • #26
berkeman said:
Anybody else notice the irony in his avatar choice? Maybe doghouses can fly better without wings? o0)

View attachment 274545
Yes, I did - and we all know what kept Snoopy's doghouse aloft, don't we?
[edit]
His imagination.
 
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1. What is the engineering paradox of weight and thrust/weight?

The engineering paradox of weight and thrust/weight refers to the relationship between the weight of an object and the amount of thrust needed to lift it. In order for an object to overcome the force of gravity and stay in flight, the thrust produced by its engines must be greater than or equal to its weight. This creates a paradox because the more thrust needed to lift a heavier object, the more weight it must carry, which requires even more thrust.

2. How is this paradox addressed in aircraft design?

Aircraft designers address this paradox by carefully considering the weight of each component of the aircraft and optimizing the design to minimize weight while still providing enough thrust to achieve flight. This often involves using lightweight materials and efficient engine designs.

3. What happens if the thrust/weight ratio is not balanced?

If the thrust/weight ratio is not balanced, the aircraft will not be able to overcome the force of gravity and will not be able to achieve flight. This can result in the aircraft being unable to take off or maintain altitude, and potentially leading to a crash.

4. How does altitude affect the engineering paradox of weight and thrust/weight?

As altitude increases, the air becomes thinner, meaning there is less air for the engines to generate thrust. This means that the thrust/weight ratio must be carefully considered and adjusted as the aircraft climbs to maintain flight. In some cases, aircraft may need to reduce weight or increase engine power in order to maintain a balanced ratio.

5. Are there any other factors that can affect the engineering paradox of weight and thrust/weight?

Other factors that can affect the engineering paradox of weight and thrust/weight include temperature, humidity, and wind conditions. These factors can impact the performance of the engines and the lift generated by the wings, requiring adjustments to be made to maintain a balanced ratio and ensure safe flight.

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