The Program Manager closed the job charge number before the engineers could finish designing the trailing edges.
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Scroll down about half way after going to this link:
https://history.nasa.gov/SP-60/ch-3.html
Excerpt:
A phenomenon is encountered in which the vertical tail loses ability to stabilize the airplane and the nose tends to yaw. Indeed, the only previous airplanes that had been flown to Mach numbers above 2 - the X-1A and X-2 - had experienced such large decreases in stability that the pilots lost control (disastrously, in the case of the X-2) when they maneuvered the craft to angles of attack of only 5 or 6 degrees. Yet the reentry maneuver of the X-15 would normally require it to operate at an angle of attack of 20 to 25 degrees.
The initial solution, proposed by NACA, was found in the large, wedge-shaped upper-and-lower vertical-tail surfaces, which are nearly symmetrical about the aft fuselage. A wedge shape was used because it is more effective than the conventional tail as a stabilizing surface at hypersonic speeds. A vertical-tail area equal to 60 percent of the wing area was required to give the X-15 adequate directional stability. Even this was a compromise, though, for weight and different flight conditions. As an additional factor of safety, therefore, panels that could be extended outward, thus increasing the pressure and stabilizing forces, were incorporated in the vertical tails. These panels -another NACA proposal- also serve as speed brakes, and the pilot can use them at any time during flight. Both braking effect and stability can be varied through wide ranges by extension of the speed brakes and by variable deflection of the tail surfaces. The large size of the lower vertical tail required for adequate control at high angles of attack required provision for jettisoning a portion of it prior to landing, since it extends below the landing gear.
A disadvantage of the wedge shape is high drag, caused by airflow around its blunt aft end. This drag force, when added to the drag from the blunt aft ends of the side fairings and rocket-engine nozzle, equals the entire aerodynamic drag of an F-104 jet fighter.
