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

3. headwind will increase the distance needed to descent 50m

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?

• IF "constant speed" in the question means constant IAS, then answer #1 is correct IF "gradient of climb" is defined relative to the ground, but #4 is correct IF "gradient of climb" is defined as relative to the air. If "constant speed" means constant groundspeed, then #4 is correct. I don't know what definitions the German test is based on, but in the real world, a headwind gives you a better climb gradient & a tailwind a worse one; "gradient of climb" that's NOT related to the ground is useless until whatever correction that does relate it to the ground gets applied. I'd have answered #1. Sep 12 '16 at 15:29
• @RalfJ my thoughts, precisely. Thus I'm confused! Sep 13 '16 at 7:16
• I found this thread over on PPRuNe discussing the difference between climb gradient and flight path angle. It seems that under EASA "gradient" is used for aircraft performance data and is expressed with reference to the air. When used in reference to the ground for obstacle clearance they apparently prefer "flight path angle." This is apparently different from FAA usage which uses gradients for some things and angles for others. Sep 16 '16 at 20:19
• If you climb a flight of stairs on a cruise ship traveling at 50 kts, does the speed of the cruise ship affect how steep the stairs are? Feb 20 '18 at 13:23
• Headwind and tailwind matter. An aircraft with a 40mph stall cruising into a 50mph head wind will appear to climb vertical, like a helicopter. (This is often the case with Super Cubs in Alaska). "Assuming the gradient of climb is indeed the same as the angle of climb". I have had approaches into 35mph winds where I nearly landed vertical - taxing was another issue. Feb 20 '18 at 14:04

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:

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.

• You're right when the horizontal distance is measured relative to the air. As I pointed out in my question this does not make sense to me as I think it should be measured relative to the ground. Sep 12 '16 at 12:59
• Well I thought it did. For me it is an important figure to know to determine if I can climb over an obstacle without starting to circle or not. Or if I can fly a SID which requires a certain climb gradient. If there is headwind, I will be able to do a higher climb gradient (in my understanding). Would you disagree with me on that? I can't grasp the context you're getting here, I'm sorry... Sep 12 '16 at 13:39
• Your thinking is correct, you do need to take headwinds and tailwinds into account when calculating obstacle clearance. This article may help: expertaviator.com/2011/02/03/…
– GdD
Sep 12 '16 at 13:53
• Your stated definition does not support the part of your answer that is key to answering the OP's question, "horizontal distance through the air, not over the ground." Do you have a source to support that part of your answer? Sep 12 '16 at 15:31
• So, looking at the formula which you posted from your link, the term "Horizontal Distance" needs to be properly defined in order to determine the answer. In my mind, "Horizontal Distance" would be measured across the ground, in which case the wind would indeed change it. It's an ambiguous term as it is now. Sep 16 '16 at 3:35

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).

• Do you have any evidence that this is how the question (or how ICAO) intended to use the term "climb gradient". Some things are measured relative to the air, and some relative to the ground. We're trying to figure out which one this is. Neither is "right" per se, it's just the one is the correct definition and usage of the word... So we kind of need a dictionary or an official definition (and a link to it if you have it.) Sep 16 '16 at 1:58
• Ability to climb over a storm, ability to clear traffic, ability to clear turbulence, it's not all about clearing obstacles that are just on the ground. All of the above often exist in the same air mass you are in, so you need to know your climb rate relative to the air to clear them. But again, I have no idea how the definition is intended to be used (because both are useful in certain circumstances), it's why I said it's important we link an authoritative definition. Sep 16 '16 at 2:03
• That's some good research, thank you! Sep 16 '16 at 5:20

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.

• Absolutely true. An aircraft with a 50mph stall cruising into a 60mph head wind will appear to climb vertical. "Assuming the gradient of climb is indeed the same as the angle of climb". I have had approaches into 35mph winds where I nearly landed vertical - taxing was another issue. Feb 20 '18 at 14:01

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.

• The change in pitch from headwind gust is only temporary. In a steady headwind, pitch to the horizon is the same as no headwind, its the angle of ascent WRT ground that changes, ergo, rate of ascent does not change. May 12 at 17:06

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.

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)

• Please use a spell checker; as this answer stands, it's very hard to read. What does this add over the other answers? The point is whether airspeed or groundspeed should be used to determine the gradient; thus answer assumes groundspeed without any reference. Nov 18 '17 at 16:37