# Difference between Best Rate of Climb and Maximum Rate of Climb?

Is there a difference between Best Rate of Climb and Maximum Rate of Climb?

From my research, best rate of climb trades ground distance for altitude (i.e. steeper climb, more altitude per unit time). Since an aircraft cannot climb faster than its max rate, these appear to be two different labels for the same concept.

Am I missing some nuance between the two?

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Generally when GA pilots talk about climb performance we speak of two different airspeed values:

Best Rate of Climb speed (Vy) gets you the most altitude per unit time (feet per minute).
When you want to get to cruise altitude quickly for maximum efficiency you'll aim for the best rate of climb so you spend the least time at lower, less efficient altitudes.

Best Angle of Climb speed (Vx) gets you the greatest altitude per unit of ground distance (feet per mile).
When you've got a FAA-Standard 50-foot-tree at the departure end of the runway you'll aim for the best angle of climb to ensure you don't wind up in the tree.

Those speeds are useful to us as pilots, but the exact rate of climb (feet-per-minute) for those speeds will vary: A fully loaded plane will climb more slowly than one that's just got the pilot and a few gallons of fuel on board, and that's where the "maximum rate of climb" enters into the discussion:

Maximum rate of climb is the number of feet per minute you can get climbing at the "best rate of climb" airspeed.

If someone is being sloppy in their usage "Maximum Rate of Climb" could mean "Best Rate of Climb" (pitch for Vy and you get what you get), but if you're being precise in your usage and really talking about the rate of climb it would mean the theoretical maximum rate of climb in feet per minute based on the current conditions and aircraft weight.

Maximum rate of climb under a given set of conditions is useful information to know if you need to clear terrain at some point on your flight path and want to be sure you can climb fast enough to do so: If you're starting from sea level and need to clear a 5000 foot mountain that's 5 minutes away but your plane can't manage more than 500 feet per minute at best-rate-of-climb speed under the current conditions you'll need to reconsider your flight plan to either avoid the mountain or climb in a circle somewhere until you can clear it.

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To help remember which is which, I imagine a chart where the x-axis is distance, and the y-axis is altitude. If distance (x) is a concern, then use Vx to minimize the x value for a given y. If reaching a given altitude (y) quickly is your primary concern, then use Vy. I imagine this is the origin of the notation as well. –  Steve N Aug 27 '14 at 18:26
An alternative memory device: the letter x has a lot of angles. –  200_success Aug 27 '14 at 21:24

Although voretaq7 has already nicely answered it, I wanted to present a picture worth thousand words.

## VX

Best angle of climb speed

The greatest gain in altitude over a given horizontal distance. VX is used to clear 50' obstacles and so forth.

## VY

Best rate of climb speed

The greatest gain in altitude over a given amount of time. VY is used on normal takeoffs and such.

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I always liked this image. What's the difference between Vx and Vy? "At Vy you'll crash through the middle of the tower, but at Vx you'll just clip the antenna masts!" –  voretaq7 Aug 27 '14 at 19:06
Shouldn't the aircraft climbing at $V_y$ be higher? –  user2168 Aug 31 '14 at 7:06

Depends what is best in the particular case. Generally, best means highest climb speed, but there might be other things which should be optimized:

• highest flight path angle: This might be desired to avoid noise on the ground, or to escape unfriendly fire near the airport. For propeller aircraft, the optimum lift coefficient is $$c_L = \frac{T\cdot\pi\cdot AR\cdot \epsilon}{4\cdot m\cdot g} + \sqrt{\left( \frac{T\cdot\pi\cdot AR\cdot \epsilon}{4\cdot m\cdot g}\right)^2 + \pi \cdot AR \cdot \epsilon \cdot c_{D0}}$$
• lowest fuel consumption per altitude gained: The highest climb speed is reached with full power, but maybe a lower power setting is more economical. In general, this is very close to the schedule with maximum climb speed. For propeller aircraft, the optimum lift coefficient for highest climb speed is the same as for minimum energy loss: $$c_L = \sqrt{3 \cdot \pi \cdot AR \cdot \epsilon \cdot c_{D0}}$$
• highest energy gain (the sum of both altitude and speed gain is optimized): This is desired when you want to reach a point far up in a hurry, like a supersonic interceptor would.

The graph below shows lines of equal total energy (black, dashed) and of maximum altitude for given climb speeds over true airspeed (blue, solid). The red line connecting the tops of the blue lines gives the flight schedule for fastest altitude gain, and the green line cutting through the blue lines at their maximum of total energy gives the schedule for the total energy gain climb. The higher you fly, the wider is the difference in optimum speed between both.

Nomenclature:
$c_L \:\:\:$ lift coefficient
$T \:\:\:\:$ thrust
$m \:\:\:\:$ aircraft mass
$g \:\:\:\:\:$ gravity
$\pi \:\:\:\:\:$ 3.14159$\dots$
$AR \:\:$ aspect ratio of the wing
$\epsilon \:\:\:\:\:$ the wing's Oswald factor
$c_{D0} \:$ zero-lift drag coefficient

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Peter Kampf: single-handedly proving math is used after high school! –  CGCampbell Aug 27 '14 at 20:54