# How did shortening the 707 increase its range?

According to the Wikipedia entry for the 707-120:

The 707-138 was a −120 with a fuselage 10 ft (3.0 m) shorter than the others, with 5 ft (1.5 m) (three frames) removed ahead and behind the wing, giving increased range. Maximum takeoff weight was the same 247,000 lb (112,000 kg) as the standard version

With the same MTOM between the -120 and the -138, what made the difference in the range? Was it simply less parasitic drag from the shorter fuselage?

I would presume that the fuel capacity (stored in the wings - center section tanks didn't come about until the -320) would have been the same.

I see notes on the -120B which switched to the P&W JT3D-1 engines which were more fuel efficient. That would account for greater range, but that doesn't apply to the -138 (at least not at launch).

• Could it be as simple as less fuselage mass means you can fill up the tanks more if the (unchanged) MTOM rather than tank volume is the limiting factor? Jan 31, 2019 at 16:11
• – user14897
Jan 31, 2019 at 16:27

MTOW is Empty Weight + Payload + Fuel Weight, and is limited by aircraft geometry factors. For a shortened aircraft, empty weight will be lower, which means either more payload or more fuel weight allowed. Some aircraft are payload limited at their extreme range.

Range is a function of MTOW and empty weight, according to the Breguet Equation for a jet: $$R=\frac{V}{c_T} \cdot \frac{L}{D} \cdot ln\frac{W_i}{W_i-W_f}$$

with $${c_T}$$ = specific fuel consumption, $$W_i$$ = initial weight, $$W_f$$ = fuel weight.

For a given fuel fraction and engine type, the primary operational parameter in the equation is L/D: the drag polar. Shortening the fuselage will indeed lower the $$C_{D0}$$ as OP states. Torenbeek section 5.3.1 gives some statistical data for high subsonic jets of the B707 era:

• Typical $$C_{D0}$$ = 0.014 - 0.020
• $$C_D$$ (including induced) = 0.02 - 0.12

At the same speed, engine type, MTOW (and L), fuel weight: a reduction of D of 10% results in an increase in range of about 10%.

• A random drive-by upvote of the question got me to notice that I'd never accepted an answer... Feb 14, 2020 at 13:45

If the fuse was shortened that much (reducing both the weight of the airframe and its cargo-carrying capacity) and the maximum takeoff weight stayed the same, the most natural explanation is that the plane's allowable fuel load at takeoff or the tank's capacity was increased.

• Notice the robustly overdesigned wings and tail of the 707 readily allowed shortening of the fuselage. An interesting study would be shortening vs thinning (reduction of cross section) of fuselage. Aug 4, 2019 at 11:45
• Also a shortened fuselage has a higher thickness ratio so in theory it could be made of lighter components while supporting the same loads. In practice this is not done for production economics, as it would be more practical to up rate the strength rating rather than what amounts to creation of an entirely new plane. Shortening also allows higher rotation angles for takeoff and landing so it could be a factor in runway length limits.(as it is with 737-900 vs -700) Feb 19, 2020 at 22:48