# How can we prove that Thrust-to-weight ratio depends by max speed?

Raymer (see source below) affirms "Thrust-to-weight ratio is closely related to maximum speed". Why? How can we demonstrate it?

Source: Daniel P. Raymer Daniel P. Raymer "Aircraft Design: A conceptual Approach" Chapter 5, Paragraph 5.2 "THRUST-TO-WEIGHT RATIO" Subparagraph "Statistical Estimation of T/W" page 80.

• This reads like an essay prompt. What work have you done on this topic and what are your thoughts? – grfrazee Mar 21 '16 at 21:55
• I would say that thrust-to-weight ratio has little to nothing to do with maximum speed from a mathematical point of view. It is only related in that a high t-to-w ratio means that there is a big engine. – hazzey Mar 22 '16 at 1:23

## 2 Answers

First I'm going to use Wikipedia to disprove the statement:

Plane    |   T/W   |  Mach (max)
------------------------------
Concorde |   0.373 |  2.04
Typhoon  |   1.15  |  Mach 2 Class
F-15C    |   1.07  |  2.5
Harrier  |   1+    |  0.95


There will be some irregularities because most of the planes in the list are military and exact numbers may not be known. Even taking that into account, there is no correlation between thrust-to-weight ratio and max speed. This is because at max speed, aerodynamic resistance (drag) is the biggest force. This is based on aircraft design, not engine size or plane weight.

Now, what your quote was probably saying was something along the lines of "... neglecting drag, thrust to weight ratio is closely related to maximum speed"

This is backed up by this link to a NASA article on thrust to weight ratio where they make the exact same simplification of neglecting drag and talking only about horizontal acceleration.

• Thank you Algo, hazzey, grfrazee. Maybe it's better that I'll report the words (part regarding jets, not propeller) of Raymer in the subparagraph named Statistical Estimation of T/W: <<Statistical Estimation of T/W Table 5.1 and...provide typical values for T/W ... for different class of aircraft. These value are all at maximum power settings at sea level and zero velocity ("static")....T/W is closely related to max speed. Later in the design process, aerodynamics calculation of drag at the design maximum spees will be used, with other criteria, to establish the required T/W. ((CONTINUE)) – d.pensopositivo Mar 22 '16 at 11:33
• ((CONTINUE)) <<... For now, Tables 5.3 and.. provide curve-fit equations based upon maximum Mach number or velocity for different classes of aircraft. these can be used as a first estimate for T/W ... The equations were developed by the autor using Ref. 1 (=JANES), and should be considered valid only within the normal range of max speeds for each aircraft class>> Table 5.1: "Thrust-to-weight ratio (T/W)" for the case of Jet transport it gives "Typical installed T/W"=0.25. Table 5.3: "t/W0 vs Mmax" it uses formula T/W0=a*Mmax^c and for jet transport it gives a=0.267 C=0.363" – d.pensopositivo Mar 22 '16 at 11:51
• Supposed that when Raymer is talking about dependance of T/W from maximum speed, he is considering the almost same concept of dependance of T/W from Maximum Mach number (in particulare, if, for both case, the aircraft is at sea level with the same daily temperature), supposed that, but what are the physical link (and link of performance and need of design) which create such link between T/W and maximum speed (or max Mach number)? – d.pensopositivo Mar 22 '16 at 14:12
• This seems a lot of obfuscational verbiage to hide two simple equations: (1) For horizontal flight at any constant speed (not just maximum speed), necessarily $T/W = D/L$. (2) At zero speed at the start of takeoff, $T/W= \text{initial acceleration}$, and therefore it influences the runway length required for takeoff. I think it's rather sad that students are still being taught 50-year-old design methods based on "curve-fitting based on the outcome of your predecessors' best guesses at how to design stuff", and justified by the excuse that "the basic principle of flight haven't changed". – alephzero Mar 23 '16 at 2:26

I think the issue here is we are trying to figure out how T/W (Thrust to Weight ratio) is a function of maximum speed. However, it is the maximum speed that is a function of T/W.

T/W will determine the efficiency of the thrust of the aircraft which (in conjunction with aerodynamic drag which is a function of velocity) will determine the maximum speed of the aircraft.

That deals with the Thrust term. Now let's talk about the weight. The aircraft must also generate enough Lift to balance the Weight. The faster the velocity the higher the lift force (to a point) but that will also increase the drag which will lower the maximum speed.

So when we talk about T/W we need to remember that at steady-level flight T/W = L/D which will be indicative of the maximum speed.