Does a headwind affect the climb gradient?

Question

When studying for my German PPL exam, I came across this question:

For those that do not speak German I'll try to translate the question, but bear with me as it is kinda picky what I'm trying to get across here:

During flight on a straight track with constant speed

1. headwind will increase the gradient of climb
2. headwind will decrease the gradient of climb
3. headwind will increase the distance needed to descent 50m
4. headwind does not affect the gradient of climb at all

As you can see answer 4 is supposed to be the correct one. I disagree, so I started searching for a reason, yet I couldn't find anything useful. Let me explain my train of thoughts:

I didn't really know the "gradient of climb", I always used the two terms "angle of climb" and "rate of climb". Thus I'm trying to figure out which one the gradient of climb is. Common sense makes me think it is the same as the angle of climb (gradient does just sound like an angle). This opinion is supported by SIDs, which have a PDG (Procedure Design Gradient) that is given in percent, just like the gradient of climb.

Assuming the gradient of climb is indeed the same as the angle of climb, the only way for the "correct" answer to be confirmed is by taking the distance traveled during the climb relative to the air, not to the ground (angle of climb is defined as the height gained divided by the horizontal distance traveled in a certain amount of time). This would mean that it is used with IAS, rather than GS, which in my opinion absolutely makes no sense ("Hey look, that mountain is 10NM away, we are climbing with 600 ft/min. and going 100 KIAS and need 3500ft more to go over the top, we're all good!" - Well, add a tailwind of 25kts, the pilot would still think he's good to go but it'd result in CFIT...).

The question I have is: How is answer 4 the correct one?

Answer 1

The gradient of climb is the ratio of the increase of altitude to horizontal distance through the air, not over the ground. The definition used by the UK CAA in CAP 698 is:

Climb Gradient

The ratio, in the same units of measurement, expressed as a percentage, as obtained from the formula: - $$\text{Gradient} = \frac{\text{Change in Height}}{\text{Horizontal Distance}} \times 100 \% $$

If you have a headwind or a tailwind it makes no difference to your climb gradient because your airplane is moving relative to the air mass.

Climb gradient is not the same as rate of climb, although they are related. Rate of climb is altitude over a period of time, gradient is climb over distance travelled. There is another question which covers the difference in more detail.

Answer 2

From the FAA's Pilot Handbook the closest term used is Angle of Climb (AOC). How it differs from a jet to a prop, and that TAS and Thrust Excess ($T_E$) are the only factors.
Airbus uses the term Air Climb Gradient ($\gamma_a$) for the same thing.

Wind is not a factor.

Achieving the maximum AOC (TAS at the $T_E$, i.e., $V_y$) will ensure the aircraft is at its steepest flight path. (Note that TAS, and not GS, is used.) Any headwind then is a bonus.

Pilot frame of reference

A headwind slows down the flight (it takes longer to reach the obstacle), but the AOC ($\gamma_a$) remains the same:

The same idea is used for descents and working out the top of descent.

Ground observer frame of reference

Wind does not affect the air climb gradient as shown above, rather the ground climb gradient ($\gamma_g$).

1.3.4. Wind Effect

A constant wind component has no influence on the rate of climb, but changes the flight path.

— Airbus Flight Operations. "Getting to grips with Aircraft Performance." (2002).

Answer 3

Climb Gradient IS affected by the wind component along the flight track. Rate of Climb is not. The gradient changes with the wind because wind affects your ground speed, and gradient is basically (rate of climb)/(ground speed). Rate of Climb and Ground Speed expressed in the same units, of course.

Answer 4

If you encounter a headwind in a climb for which you want to climb at a constant IAS, with the increase in airflow relative to the aircraft you will see a rise in IAS, so to pitch for that same IAS as what you were climbing at before the headwind, you will be at a steeper angle vs the horizontal of the earth. The climb performance when it comes to rate of climb will not be changed but most definitely the angle.

For best angle of climb, i.e. Vx to clear an obstacle this would be of great help to you. The head wind will lower your ground speed thus covering less ground since Vx is by definition height gain vs ground distance covered.

Answer 5

On a lighter note, we can focus on the term "Steiggradienten".

The literal translation is "rise gradient", which could be interpreted as "rate of climb" for a given throttle setting, at a constant airspeed.

Answer 3 does deal with "Strecke" or "route or distance" traveled to sink 50 meters, but is incorrect.

When one gets away from the more widely accepted definition of gradient (rise over run) based on ground distance, then

Steiggradienten = Rate of Ascent/ Indicated Airspeed (meters/second)

This essentially is the angle to the horizon one will see for a given power and pitch setting. Headwind will not affect this, but

headwind certainly will affect groundspeed or TAS

Items we need to clear are generally fixed points on the ground.

Answer 6

Wind adverseley affected to the climb gradient( weight, IAS, Large flap setting and acceleration also). As Climb gradient is a ratio of heigh to the travelled ground distance, wind affcet has a large. As increasng altitude in steady wind condition with given IAS TAS increasing which same time decrerasing gradient. If climbing in tailwind also climb gradient is decraesing which distanve required to travell increase. With head wind climb gradient increase which decrease ground distance required to travel. Dont confuse it with Rate of Climb. Wind has no affect to ROC as roc is altitude change in unit of time.

Climb out in tailwind sometimes some pilots confuse it by setting large flap setting. But teh lage flap setting the more drag and less gradient. Best choise is (when rw is limited by lenght) use improved climb( high speed to allow creation more excess thrust)