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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?

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$V_X$ 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:

Graph illustrating relationship between thrust, drag and Vx

$D$ 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 $V_X$

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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)

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