- #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).
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).
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/
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).
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).
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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