Exercise to Calculate take-off distance on a grass runway

Juan Vela

Juan Vela

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mistervela
Hey guys, I'm getting mixed answers with this problem: (Below is the attached performance table)

Cessna C-150. Calculate the takeoff ground run and total takeoff distance on a grass runway. QNE = 2500 ft; OAT = +20 °C; Headwind = 5 Kts; Max takeoff weight; Flaps up.

The answer is: 917 ft and 1637 ft

I calculated the Ground Roll and Total take off distance by interpolating:

[1] 910-630=280; 280 / 2=140; 630+140=770ft for Ground Roll
[2] 1660-1250=410; 410/2 = 205; 1250+205 = 1455 ft for Total Take off
[3] For a grass runway: 7% of 1455 = 101.85
[4] ISA Temperature at 2500ft = 15-2(2500/1000) = 10c = 50F
[5] OAT = +20c = 68F
[6] Difference between ISA and OAT @2500 in F = 68-50 = 18F
[7] 10% for each 35F above ISA = 5.14% for 18F

Final Answer:
770 * 1.0514 +101.85 = 911 and 1455*1.0514 + 101.85 = 1631.6

911 and 1631 are nowhere close to 917 and 1637, am I missing something?
 

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Your numbers are close.
Should the grass fudge factor be be added before the temperature fudge factor is applied? That will get you the missing 6 feet.

Edit: the question is asked to encourage you to think about why we correct for temperature.
 
Last edited:
champ driver said:
I have no idea what all those numbers are from and how you worked it out.
In the real world there are so many variables on a grass runway, length of grass, wet or dry, slope, temp and elevation, no factory chart is going to be very accurate.
Click to expand...
Check the attached/embedded performance table.
 
Do the adjustments in the order shown on the chart. Temperature is #1, grass is #2.
 
Clark1961 said:
Your numbers are close.
Should the grass fudge factor be be added before the temperature fudge factor is applied? That will get you the missing 6 feet.

Edit: the question is asked to encourage you to think about why we correct for temperature.
Click to expand...
The question is aimed to know why my results don't match the final answer of the multiple choice question. Somebody could do it from scratch.
 
Juan Vela said:
The question is aimed to know why my results don't match the final answer of the multiple choice question. Somebody could do it from scratch.
Click to expand...
Okay, I'll change tactics.

Why do we correct both roll and obstacle clearance for temperature?
 
MauleSkinner said:
Is the wrong answer closer?
Click to expand...
The answer is 917 and 1637 and my results are 911 and 1631. Very close but I'm may be missing something. It's got to be precise because the other answers in the selection are close too, like 910 and 1600, etc.
 
Juan Vela said:
The answer is 917 and 1637 and my results are 911 and 1631. Very close but I'm may be missing something. It's got to be precise because the other answers in the selection are close too, like 910 and 1600, etc.
Click to expand...

Clark and I both posted how to get the correct answer...o_O
 
Welcome to "bad question land", by the way...whether you multiply by 1.07 or 1.0514 first shouldn't matter...

770 * 1.07 * 1.0514 is exactly equal to
770 * 1.0514 * 1.07

The fact that the wrong answer is closer because of an insignificant rounding difference makes it a bad question.

Id be willing to bet that the half dozen takeoffs used to extrapolate the data varied by more than 6 feet from the book result.
 
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MauleSkinner said:
Welcome to "bad question land", by the way...whether you multiply by 1.07 or 1.0514 first shouldn't matter...

770 * 1.07 * 1.0514 is exactly equal to
770 * 1.0514 * 1.07.
Click to expand...

While the above is a mathematically true statement, it does not follow the instructions in the POH. The table says for grass runway to add 7% of the 50' obstacle distance to each of the ground roll and the 50' obstacle distance. So you have to calculate the correct 50' distance first, including the temperature adjustment, to determine the adjustment for a grass runway. Also, OP calculated each adjustment separately and then added them together. Wrong.

The grass runway adjustment is 1455 * 1.0514 * 7% = 107.1, not 101.85
 
True enough...I guess I should be using something bigger than an iPhone to look at charts, even with bifocals. ;)
 
Skip the question - it's not worth your time. Or, just guess. The "lesson" is to know grass is a "draggier" surface, and you'll need more room than a paved runway. But I have noticed over the years that grass is not homogeneous; sometimes it is longer, sometimes shorter. Sometimes the dirt under it is softer. Or harder, or not level. The grass can even be wet.
 
Glad you're trying to be that precise. It's an interesting mental exercise, but...

As far as the real world goes, pick a percentage even higher and add that on for both, lest you find yourself wondering why those trees are getting so big in the windshield. Add a safety margin.

At least add it, until you know damn well the airplane you're flying will even come close to book numbers both because the airplane probably won't, and then there's your skill level...

Some folks here can tell stories of grass runways that had a small lake in the middle of them that nobody could really see, and plowing a twin through said small lake... or so I've heard... cough... Ted... LOL.
 
"1455 * 1.0514 * 7% = 107.1, not 101.85"

107.1 and 1455 are written with four significant digits. 1.0514 is written as if it had five freeking significant digits. That would mean that you know the value of that factor to within 0.01% of the actual value. NFW.

On the other hand, the book says 7%. Not 7.0% Not 7.00%. And sure as heck not 7.0000%. It says 7%. One significant digit. Only accurate to within about 10% at best. Not 1%. Not 0.1% and not 0.01%. The precision just isn't there. Pretending it is there is wrong and, in come cases, can lead you to making the wrong conclusions.

Real answer: The answer is 100 Period. Not 107.1 (four significant digits), not 101.85 (five significant digits), not 101. or 107 (three). 100 plus or minus quite a bit.

What kind of stupid test is this question from?
 
Juan Vela said:
Hey guys, I'm getting mixed answers with this problem: (Below is the attached performance table)

Cessna C-150. Calculate the takeoff ground run and total takeoff distance on a grass runway. QNE = 2500 ft; OAT = +20 °C; Headwind = 5 Kts; Max takeoff weight; Flaps up.

The answer is: 917 ft and 1637 ft

I calculated the Ground Roll and Total take off distance by interpolating:

[1] 910-630=280; 280 / 2=140; 630+140=770ft for Ground Roll
[2] 1660-1250=410; 410/2 = 205; 1250+205 = 1455 ft for Total Take off
[3] For a grass runway: 7% of 1455 = 101.85
[4] ISA Temperature at 2500ft = 15-2(2500/1000) = 10c = 50F
[5] OAT = +20c = 68F
[6] Difference between ISA and OAT @2500 in F = 68-50 = 18F
[7] 10% for each 35F above ISA = 5.14% for 18F

Final Answer:
770 * 1.0514 +101.85 = 911 and 1455*1.0514 + 101.85 = 1631.6

911 and 1631 are nowhere close to 917 and 1637, am I missing something?
Click to expand...

You can't reverse step 1 and 2 in the notes, which is what you did in your math.
 
Capt. Geoffrey Thorpe said:
"1455 * 1.0514 * 7% = 107.1, not 101.85"

107.1 and 1455 are written with four significant digits. 1.0514 is written as if it had five freeking significant digits. That would mean that you know the value of that factor to within 0.01% of the actual value. NFW.

On the other hand, the book says 7%. Not 7.0% Not 7.00%. And sure as heck not 7.0000%. It says 7%. One significant digit. Only accurate to within about 10% at best. Not 1%. Not 0.1% and not 0.01%. The precision just isn't there. Pretending it is there is wrong and, in come cases, can lead you to making the wrong conclusions.

Real answer: The answer is 100 Period. Not 107.1 (four significant digits), not 101.85 (five significant digits), not 101. or 107 (three). 100 plus or minus quite a bit.

What kind of stupid test is this question from?
Click to expand...
You really need to ask? The FAA, of course.
 
Ok, so the question suggests an undue precision in the calculation. That's poor question writing by the FAA.

But I'm curious about something written not by the FAA, but by Cessna: The footnote in the POH specifies that grass causes a 7% increase in the total distance to clear a 50' obstacle. Why did Cessna present it that way, instead of a percentage increase in the Ground Run? The grass couldn't possibly make a difference in the climb once the plane is airborne.
 
NoHeat said:
Ok, so the question suggests an undue precision in the calculation. That's poor question writing by the FAA.

But I'm curious about something written not by the FAA, but by Cessna: The footnote in the POH specifies that grass causes a 7% increase in the total distance to clear a 50' obstacle. Why did Cessna present it that way, instead of a percentage increase in the Ground Run? The grass couldn't possibly make a difference in the climb once the plane is airborne.
Click to expand...
Probably because of the variability in the drag of "grass". Seven percent is the lowest number I've seen for grass or turf conversion...Ten is also used frequently, and occasionally I've seen a higher number for "long grass".

Keep in mind, too, that this factor is based on the same technique used on hard surface runways, and does NOT include accommodation for soft field technique.
 
NoHeat said:
But I'm curious about something written not by the FAA, but by Cessna: The footnote in the POH specifies that grass causes a 7% increase in the total distance to clear a 50' obstacle. Why did Cessna present it that way, instead of a percentage increase in the Ground Run? The grass couldn't possibly make a difference in the climb once the plane is airborne.
Click to expand...
Because the book was written by someone with a degree in English or Journalism and not Engineering?

Or, perhaps, someone just hadn't had enough coffee that morning.
 
Capt. Geoffrey Thorpe said:
"1455 * 1.0514 * 7% = 107.1, not 101.85"

107.1 and 1455 are written with four significant digits. 1.0514 is written as if it had five freeking significant digits. That would mean that you know the value of that factor to within 0.01% of the actual value. NFW.

On the other hand, the book says 7%. Not 7.0% Not 7.00%. And sure as heck not 7.0000%. It says 7%. One significant digit. Only accurate to within about 10% at best. Not 1%. Not 0.1% and not 0.01%. The precision just isn't there. Pretending it is there is wrong and, in come cases, can lead you to making the wrong conclusions.

Real answer: The answer is 100 Period. Not 107.1 (four significant digits), not 101.85 (five significant digits), not 101. or 107 (three). 100 plus or minus quite a bit.

What kind of stupid test is this question from?
Click to expand...
While you are going off on your rant remember to carry all digits through the calculations and then round once the final value is obtained.
That is all. Return to your pointless rant.
 
Capt. Geoffrey Thorpe said:
"1455 * 1.0514 * 7% = 107.1, not 101.85"

107.1 and 1455 are written with four significant digits. 1.0514 is written as if it had five freeking significant digits. That would mean that you know the value of that factor to within 0.01% of the actual value. NFW.

On the other hand, the book says 7%. Not 7.0% Not 7.00%. And sure as heck not 7.0000%. It says 7%. One significant digit. Only accurate to within about 10% at best. Not 1%. Not 0.1% and not 0.01%. The precision just isn't there. Pretending it is there is wrong and, in come cases, can lead you to making the wrong conclusions.

Real answer: The answer is 100 Period. Not 107.1 (four significant digits), not 101.85 (five significant digits), not 101. or 107 (three). 100 plus or minus quite a bit.

What kind of stupid test is this question from?
Click to expand...
Probably not the way it was calculated at the factory, however...they probably used "slide rule accuracy" to determine the number of digits used...for multiplication and division use three digits following a 1, two digits following any other number.

7% of 1455 would be 1455*.0700=101.9, which would be added to 1455 to get 1557; multiplying by 1.07 instead would be 1455*1.070=1556.

Yet another issue that makes it a bad question...not only do you have to know the order in which the test writers calculated, but this is likely different from the way Cessna did it.
 
This isn't an FAA question. I think OP is from another country.
 
Clark1961 said:
While you are going off on your rant remember to carry all digits through the calculations and then round once the final value is obtained.
That is all. Return to your pointless rant.
Click to expand...
Carrying thru all digits is irrelevant for most things except proving to teachers you can multiply many numbers together for a grade. Mathematicians (I is one, or used to be one) live with the issue of accuracy/inaccuracy (significant digits) because the answer is only guaranteed to the significant digits of the values being multiplied (multiplicands), not the answer e.g. 1.2 * 1.4 = 1.68 That 8 cannot be guaranteed, not on a calculator nor a computer (ref: IEEE 754, explaining issues with hardware and base 2 ) because there is only 1 significant digit in each of the multiplicands. So taking a calculation out many digits is really irrelevant.

Put it another way, consider 1.2 * 1.47 = 1.764. But there's only 1 and 2 significant digits in the multiplicands, so by rules of significant digits, the answer can only be assured to the number of least significant digits, or 1. So you have the choice to either round up or down to 1.8 or 1.7. When working with an airplane, I'll always round up (and add 10% for this, another 7% because the sun is shining, another 5% for that...) for safety.
 
I only have a handful of grass takeoffs and landings, but I found in my experience that the plane felt tremendously slower on the ground on grass, much more so than merely a 7% increase. It honestly almost felt like full power was barely enough to get it moving... I didn't like it
 
Old thread, but in case someone is reading this thread, looking for the actual calculations to this problem. It's been hinted around in the discussion above, but the short answer is, the OP's increase in distance due to grass was adjusted before the altitude adjustment when he should've adjusted for altitude 1st. The full answer is:

[1] Extrapolation for GROUND ROLL from the table for 5kt headwind: 910-630=280 ; 280/2=140 ; 630+140= 770ft
[2] Extrapolation for TAKEOFF from the table for 5kt headwind: 1660-1250=410 ; 410/2=205 ; 1250+205= 1455ft

[3] Calculate GROUND ROLL for temp correction: OAT in the question=+20c=68f ; 68f-50f=18f above standard temp ; adjustment in chart say 1% increase in distance for every 3.5f ; 18/3.5= 5.1429% ; 770ft * 1.051429= 809.6ft
[4] Use same 5.1429% in step 3 to calculate TAKEOFF distance: 1455ft * 1.051429= 1529.8ft

[5] From chart: for a grass runway, increase both numbers by 7% of TAKEOFF distance: 7% of 1529.8ft= 107.09ft
[6] GROUND ROLL adjusted for grass: 809.6+107.09= 916.69ft
[7] TAKEOFF adjusted for grass: 1529.8+107.09= 1636.9ft

Final Answer:
Ground roll = (770 * 1.051429)+107.09= 916.69
Takeoff over 50' obstacle = (1455 * 1.051429)+107.09= 1636.9

The answer on the OP's test has rounded the two answers off to the nearest whole numbers - 917ft and 1637ft
 
Skeptical John said:
Old thread, but in case someone is reading this thread, looking for the actual calculations to this problem. It's been hinted around in the discussion above, but the short answer is, the OP's increase in distance due to grass was adjusted before the altitude adjustment when he should've adjusted for altitude 1st. The full answer is:

[1] Extrapolation for GROUND ROLL from the table for 5kt headwind: 910-630=280 ; 280/2=140 ; 630+140= 770ft
[2] Extrapolation for TAKEOFF from the table for 5kt headwind: 1660-1250=410 ; 410/2=205 ; 1250+205= 1455ft

[3] Calculate GROUND ROLL for temp correction: OAT in the question=+20c=68f ; 68f-50f=18f above standard temp ; adjustment in chart say 1% increase in distance for every 3.5f ; 18/3.5= 5.1429% ; 770ft * 1.051429= 809.6ft
[4] Use same 5.1429% in step 3 to calculate TAKEOFF distance: 1455ft * 1.051429= 1529.8ft

[5] From chart: for a grass runway, increase both numbers by 7% of TAKEOFF distance: 7% of 1529.8ft= 107.09ft
[6] GROUND ROLL adjusted for grass: 809.6+107.09= 916.69ft
[7] TAKEOFF adjusted for grass: 1529.8+107.09= 1636.9ft

Final Answer:
Ground roll = (770 * 1.051429)+107.09= 916.69
Takeoff over 50' obstacle = (1455 * 1.051429)+107.09= 1636.9

The answer on the OP's test has rounded the two answers off to the nearest whole numbers - 917ft and 1637ft
Click to expand...

Are you sure? You seem a bit skeptical.
 
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