# Why is the initial short-field climb below Vₓ in a Cessna 172?

Short-field takeoff procedure for a Cessna 172R is

1. Wing Flaps – 10°.
2. Brakes – APPLY.
3. Throttle – FULL OPEN.
4. Mixture – RICH …
5. Brakes – RELEASE.
6. Elevator Control – SLIGHTLY TAIL LOW.
7. Climb Speed – 56 KIAS (until all obstacles are cleared then $V_y$).
8. Wing Flaps – RETRACT slowly after reaching 60 KIAS.

However, best angle-of-climb or $V_x$ at is 62-67 KIAS depending on elevation. Why is the first stage of the climb slower than $V_x$, and if the slower speed gives better performance, then why isn’t that the published figure?

$$V_X$$ published in the manual is $$V_X$$ for flaps up. $$V_{X_{F10}}$$ will be slower than $$V_{X_{UP}}$$. Most likely, the speed in the procedure is, or is very close to $$V_{X_{F10}}$$.

$$V_X$$ (speed for angle of best climb) occurs where the excess thrust ($$T$$ - $$D$$) is the highest. Refer to the graph below: $$D$$ is Induced drag ($$D_I$$, varies with $$\frac{1}{v^2}$$) + Parasite drag ($$D_P$$, varies with $$v^2$$). By extending the flaps, you are increasing only $$D_P$$ and the graph describing $$D$$ ($$D_{tot}$$ in the graph) moves upwards to the left. This means that the point for $$V_{MD}$$ moves to the left. Since $$V_X$$ is found at max $$T - D$$ it varies with thrust too (which will vary differently, depending on the type of propulsion system), and is not automatically found at $$V_{MD}$$, but the two speeds generally move together in the same direction.

There's also another, albeit marignal, effect (that i did not put in the graph) to take into consideration for the first 10-20 ft, and that's the ground effect. In ground effect, the aircrafts $$D_I$$ will be lower, further moving the $$D$$ graph to the left, and downwards, resulting in a lower $$V_{MD}$$, and therefore generally also lower $$V_X$$

The published Vx is in the clean condition (no flaps): 62.

With the flaps down, for a short-field takeoff, Vx is 56.

This is the same reason why the stall speed (bottom of the white arc) is lower with flaps than without (bottom of the green arc)