Performance Speeds

We start our pilot journey flying general aviation aircraft knowing speeds such as best angle of climb, best rate of climb, best glide, etc... by heart.

In the frantic race of airline training, somehow all this practical knowledge was lost, replaced by 'the profile'.

Flying the profile is the usually the best way, and there are other limitations and policies to comply with, yet having a working knowledge of key performance speeds comes in handy in certain situations.

Best Angle of Climb (V_x)

Suppose you are lined up on the runway looking straight at a mass of convective clouds in your path. Perhaps the best course of action is to gain as much altitude, in as short a distance as possible to limit exposure to the turbulence.

For a turbojet aircraft, V_x occurs at (L/D)_max.

Best Rate of Climb (V_y)

Suppose you are in Denver with an approaching cold front. There is a south westerly wind blowing across the rocky mountains creating all sorts of bumpy turbulence from take off up to the beginning of the flight levels. There is no way around it, but it would be nice to get through it as fast as possible.

Determining the speed for best rate of climb requires knowing the power available and power required curves as well as the weight. It can also be calculted knowing the thrust available and drag created at a given speed.

Jet engines produce constant thrust with speed. They create more power as speed increases. Because the thrust to weight and drag ratio of an aircraft can vary depending on design, there is no rule of thumb to relate this speed to (L/D)_max. Underpowered aircraft may be only slightly faster. High powered aircraft will be significantly faster.

Best Range

There are two facets to best range performance. The first is to operate the flight with minimum fuel expenditure. This is not always the most profitable speed however. The profitability of a flight must also consider the time costs of airframe maintenance, crew pay, and being on time. Many airlines use a cost index program to optimize fuel burn costs vs flight time costs.

The other facet of best range performance is extracting the furthest range out of a given amount of fuel. This becomes predominant when poor weather or unforecast headwinds push the margins of fuel reserves.

Best Range is generally achieved about 1.33 times (L/D)_max.

Best Endurance

This is the speed we want to be at when we are holding so that we can conserve the most amount of fuel until our further clearance time.

The speed for best endurance is achieved at (L/D)_max.

It can be verified when the fuel burn rate is at it's minimum, while maintaining a constant speed and altitude.

Best Glide (Minimum Angle of Descent)

Dual engine failure at altitude in turbojet and turbofan aircraft is handled differently than a piston. The immediate action items for my aircraft are continuous ignition ON, and airspeed not less than 240KIAS. 240KIAS is much higher than best glide. It's necessary to keep air flowing through the engine so that it is continuously being cooled. If airspeed is lost, the hot, yet not operating engine will melt itself. If it melts, there is no hope of it restarting (core lock). Best glide is only appropriate once all hope of restarting the engines is lost.

For most aircraft (because engine type doesn't matter if it's not running) minimum angle of descent is achieved at (L/D)_max.

Minimum Rate of Descent

As discussed above, minimum glide is only appropriate once a deadstick landing is inevitable. Why would minimum sink be preferable to best glide? The only scenario I can think of would be a ditching at sea, where it doesn't matter where you end up, and more time aloft would be valuable to prepare the cabin, finish checklists, and make radio calls.

For most aircraft, minimum rate of descent is achieved around 75% of (L/D)_max.

Best Rate of Descent and Best Angle of Descent

Best Rate of Descent - is for losing altitude as quickly as possible, as in an emergency descent.

Best Angle of Descent - is for descending from a high altitude to a low altitude in a short distance, maybe to meet a crossing restriction or be stable on an approach.

To determine these performance speeds, we must fly speeds as far as possible from (L/D)_max.

The ideal speed for best rate is ∞kts.
The ideal speed for best angle is 0kts (a stall).

Unfortunately those speeds are not available so we will have to settle for V_MO/M_MO in both cases.

The addition of drag moves (L/D)_max slower (further away) from V_MO/M_MO. Remember, (L/D)_max is the speed of minimum drag; an equilibrium between induced and parasitic. Flight spoilers increase the parasitic drag and shift the balance point slower.

A Suggestion...

While it is important to know the limits of the aircraft, there are alternatives. Ask ATC for a circle or vectors. Wouldn't that be less chaotic, and more comfortable in the cabin? Don't get tunnel visioned into one solution to a problem when there are many.

In Summary

Performance Speeds Calculated

Using the above table, we will attempt to determine these performance speeds for a CRJ700.

To make the speeds applicable for both departure and approach phases of flight, I will select a weight of 67,000lbs which is the maximum gross landing weight, and I will use sea level values.

Manufacturer Documentation Fact Findings

AFM

Flaps 0, gear up stall speed
142 kts

Final Takeoff Climb / Enroute Climb Speed:
188 kts

FCOM Vol. 2

Recommends accelerating to 200kts until flaps up then, then 250kt climb.

Minimum maneuvering speed (stick shaker protection for 45° of bank)
186 kts

Minimum approach speed (stick shaker protection for 30° of bank)
176 kts

QRH Vol. 1

Final Takeoff Climb / Enroute Climb Speed:
188 kts

Flaps 0, Final Approach Speed:
176 kts

Minimum Drag Speed
190 kts

Best Rate of Climb Speed
248 kts

Highlighted right here are the two values which matter most to us, provided in a clear table format.

The calculated value

(rounded for simplicity)

Relation to weight and altitude

All the values derived from (L/D)_max increase with altitude and decrease with weight.

The best rate of climb speed is mostly constant with altitude, however it increases with weight.

Source:
H. H. Hurt, Jr; Aerodynamics for Naval Aviators

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