converting climb gradient % to FPM

[getonit]

Citation I manual publishes the second second climb gradient in % and I was looking for an easy way to convert that to FPM. The assumption is you are flying V2, about 102 knots and gradient would be 7%.

What I did was take Sin 7% times 102 to get 12.4 which is the vertical distance of that triangle. Then converted that to FPM by multiplying 12.4 X 6000ft/NM divided by 60 min which makes all of the units come out to 1240 FPM which seems like a reasonable number but I don't have a lot of confidence in my logic and my geometry (which was from a long time ago)

In summary looking for an easier way with out the geometry excercise. I don't see how any rules of thumb would work because of the different speeds.

Thanks.

 

[dmspilot00]

I assume that a 7% climb gradient means that your vertical distance should be 7% of your horizontal distance (the same way road and runway grades are measured)?

Don't take the sine, that's only for angles (measured in degrees or radians). You already know the vertical height of the triangle; it's 7% of the base.

At a groundspeed of 102 knots you're going (102*6076)/60 = 10,329 feet per minute. 7% of this is 723 feet. So you need to be at 723fpm at a groundspeed of 102 for a 7% climb gradient. That's if I got the definition of climb gradient correct.

 

[pilotman2105]

Citation I manual publishes the second second climb gradient in % and I was looking for an easy way to convert that to FPM. The assumption is you are flying V2, about 102 knots and gradient would be 7%.

What I did was take Sin 7% times 102 to get 12.4 which is the vertical distance of that triangle. Then converted that to FPM by multiplying 12.4 X 6000ft/NM divided by 60 min which makes all of the units come out to 1240 FPM which seems like a reasonable number but I don't have a lot of confidence in my logic and my geometry (which was from a long time ago)

In summary looking for an easier way with out the geometry excercise. I don't see how any rules of thumb would work because of the different speeds.

Thanks.

Not that I fly a Citation, but I am pretty decent at math and have done a few % gradient climbs before.

All % gradient climbs are is you must cover a percentage (in your example, 7%) of your horizontal distance. In your example, for every 100 feet of horizontal distance you travel, you must climb 7 feet.

With that, take your groundspeed in kts and divide by 60. This gives you nautical miles per minute. Multiple that result by 6,072 (approximate distance of a nautical mile). This gives you feet/minute that you are travelling horizontally. Multiply that number by .07 (7%) and you get the FPM climb required.

So for your example, here's the math:

102 knots / 60min = 1.7 nautical miles/min
1.7 nautical miles/min* 6072 feet/nautical mile=
10322.4 feet/min
10322.4 feet/min * .07 climb gradient = 722.568 FPM climb

 

[TonyC]

Citation I manual publishes the second second climb gradient in % and I was looking for an easy way to convert that to FPM.

Funny, we just covered this a few days ago...

Climb Gradient: % to FPM

>>>>>>>>> "RULE OF THUMB":

<><><><><><><><><><><><><><><><><><><><><>

Climb Rate (fpm) = Climb Gradient (%) X Airspeed (knots)

<><><><><><><><><><><><><><><><><><><><><>

(This "Rule of Thumb" ASSUMES 60.8 = 60 and groundspeed = airspeed.)

Example:

Climb Gradient = 4.5%

Airspeed = 150 knots

Climb Rate = 4.5 X 150 = 675 ft per minute

For your problem, 7% at 102 knots yields 714 fpm - - within 9 fpm of the actual answer.

 

[dmspilot00]

So, now that I know it was right, to simplify:

fpm = groundspeed (kt) * gradient (decimal) * 6076 / 60
fpm = groundspeed (kt) * gradient (decimal) * 101.3

at 7% that is

fpm = groundspeed * 0.07 * 101.3
fpm = groundspeed * 7.09

The rule of thumb TonyC cited works because the number of feet in a nautical mile is so close to 100 times the number of minutes in an hour. If you want to get really really close using the rule of thumb TonyC gave, add 1% to whatever you get. E.g. 7*102 = 714... + 7 = 721. Within 2fpm of actual answer

 

[TonyC]

If you want to get really really close using the rule of thumb TonyC gave, add 1% to whatever you get. E.g. 7*102 = 714... + 7 = 721. Within 2fpm of actual answer

If you can read the difference between 714 fpm and 723 fpm on YOUR VSI, then you better add 1 and one-third percent!

 

[getonit]

dmspilot00 you are right, I completely forgot that it is a rise/run percentage not an angular percentage which is where I went all wrong. Thanks for your help everybody.

 

[CaSyndrm]

Just go the the departure plate that gives you the gradient restriction. Then look at the FPM provided on that chart under the 100kt box. That is your angle when you move the decimal point. Then just get a weight from the performance paperwork that will give you that angle or greater.

 

[TonyC]

Just go the the departure plate that gives you the gradient restriction.

He didn't say it was a restriction from a departure plate. He SAID he was looking at second segment climb figures in the Citation I manual.

 

[A Squared]

Another way would be to look it up in a Jepp manual.

They have % gradient vs airspeed charts from 2.5% to 13% Not that there's anything wrong with the answers given, just another option for getting the answer.

 

[CaSyndrm]

quote:
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Originally posted by CaSyndrm
Just go the the departure plate that gives you the gradient restriction.
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He didn't say it was a restriction from a departure plate. He SAID he was looking at second segment climb figures in the Citation I manual.



OH! NEVERMIND!