EdFred
Taxi to Parking
The parallel you are trying to draw doesn't even make sense, or apply in this situation, not so not sure of the point.
What would you do? (Checkride)
The parallel you are trying to draw doesn't even make sense, or apply in this situation, not so not sure of the point.
MauleSkinner
Touchdown! Greaser!
The point is you’re playing a game of “you’re a ****ing idiot because I know something you don’t,” so I decided to join in.
EdFred
Taxi to Parking
I never said anything of the sort. The knowledge portion of the commercial test is on the same level of math as what I posted what I would do to determine the takeoff and 50' distance. Anyone that can pass the commercial knowledge test can do this.
MauleSkinner
Touchdown! Greaser!
But you refuse to show how to do “this”. You merely say we should know.
so…MGW takeoff distance is 2146 feet. I apply 9th grade math and come up with 1867 feet….how did I get there?
texasclouds
En-Route
All this nerd talk hurts my head. Ninth grade was a long time ago.
The original subject is getting lost in the trivia here.
What is the OP required to do? No 150% rule of thumb is going to get him through his exam with the DPE. Those rules are a waste of performance at sea level, and killer at high altitude and hot days.
I still say the old E 6 B or the app version is the best compromise, but the experts here should have something better from the digital era.
What source do you suggest, he needs something legal.
What is the OP required to do? No 150% rule of thumb is going to get him through his exam with the DPE. Those rules are a waste of performance at sea level, and killer at high altitude and hot days.
I still say the old E 6 B or the app version is the best compromise, but the experts here should have something better from the digital era.
What source do you suggest, he needs something legal.
EdFred
Taxi to Parking
No one asked me to show them how. You just asked if I could fill us in on it. I did. The math isn't hard and it's only a couple of equations where you just plug in the numbers.
If you want I can make up some Arrow like numbers and give an example of how to do it.
MauleSkinner
Touchdown! Greaser!
that would be what I would consider filling us in.thank you
MauleSkinner
Touchdown! Greaser!
Can you provide some form of instruction for those who have never been taught this?
texasclouds
En-Route
KISS, we are pylots. I had a few students that were engineering students. For their pre solo knowledge test they were required to tell me the crosswind component with a given scenario. Well they did some fancy math equations and inadvertently gave me headwind component instead of x-wind. It was a great teachable moment to show them how to use the crosswind chart. Those mundane details man.
MauleSkinner
Touchdown! Greaser!
What do you suggest for the OP’s scenario?
texasclouds
En-Route
Show DPE he knows how to utilize the charts provided. Understands basic aerodynamics and the impact of less than gross weight. Understands basic ADM and ways to mitigate risk. Understands the limitations of the provided tables, the aircraft, envirommental conditions, and the pilot. DPE will want to see his thought process and decision making skills.
I personally wouldn’t apply any rules of thumb or untested off-chart calculations with a DPE.
MauleSkinner
Touchdown! Greaser!
Ok…what impact of less than gross weight determines that there’s actually enough runway to takeoff? Theory is great, but you still have to determine that you can fly the checkride.
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Bro do you even lift
can u post a pic of the chart you do have?
texasclouds
En-Route
The extent to the additional performance is unpublished information, per OP. If the candidate finds the takeoff is unsafe with the provided charts, then should he delay flight until better temperatures allow it to work? Reposition the aircraft? Get a better job that doesn’t require him to fly old Arrows?
I think the 150% fudge factor OP mentioned is what is hurting him. Surely he isn’t testing out of a field that an Arrow at gross couldn’t depart from.
MauleSkinner
Touchdown! Greaser!
Unfortunately the candidate cannot determine whether the takeoff is safe or unsafe with the provided charts. Obviously the DPE thinks there’s “other reliable information” that can allow that determination.
texasclouds
En-Route
He found it unsafe with a 150% fudge factor added. So the question for OP is, whudya gonna do?
I was thinking through this earlier this morning and the problem with using an average acceleration is that thrust, drag, and rolling resistance all vary with aircraft velocity.
As a result, acceleration isn't linear and plugging an average acceleration into F=ma may provide wrong information that could lead to a wrong conclusion. My head hurt before I decided if that variance from reality was conservative or anti-conservative.
MauleSkinner
Touchdown! Greaser!
How much fudge factor do you feel is appropriate, and how do you make that determination?
EdFred
Taxi to Parking
As per Maulskinner's request.
Disclaimer: These numbers are pulled out of my ass, and not be to used for any sort of real world calculations and only an example of how *I* would do it.
Gross weight: 2400lbs
Takeoff roll: 800ft
Distance to clear 50': 2000'
Rotation speed: 60mph
Vx: 80mph
The above are at max gross.
Your current weight: 2000lbs
First convert to common units.
Vr: 88ft/s and
Vx ~117ft/s
The following variables and formulas are used
d = distance, v = velocity, t = time, a= acceleration, F = force m = mass (in this case we will use weight, I'm not going to use slugs)
v = at
F = ma
d = vt + 1/2at^2
We only know d and v at this point for gross weight.
But we can rearrange
v = at
so that
a = v/t and
d = vt so that
t = d/v and plug those into the d = vt +1/2at^2 formule and since we are starting from 0 we only need the 2nd half of the equation getting
d = vt/2 this can be rearranged so that
800 = 88 * t / 2
t = ~18.2 seconds
We can now determine acceleration
v = at
88 = a * 18.2
a = 4.8ft/s/s
And now what is the engine and prop doing for us:
F = ma
F = 2400 * 4.8
F = 11520lbf/s/s
Now use this to determine a at the new weight
11520 = 2000 lbs* a
a = 5.76ft/s/s
Now determine the Vspeed factor (this should have been taught somewhere before or during commercial)
sqrt(current wt/gross wt) = .91 call it .9 for ease of use and add a few % to your final numbers.
Vr = 80ft/s
Vx = 105ft/s
v = at
80 = 5.76 * t
t = 13.9 second
d = 1/2*at^2
d = 1/2*5.76*13.9*13.9
d = ~560ft
Even if we just want to use this without calculating the time to accelerate to Vx and doing calculus because of drag and all that stuff, the 50' distance is now down to 1760'
But, doing the rest of the math:
At gross it took us 6 seconds to accelerate to Vx (and lets assume we gain no vertical distance in that as a worst case)
In that 6 seconds at gross we covered another ~600ft. So we've used 800 (t/o roll) + 600ft leaving us 600' to climb 50' (it's less because we climbed during Vx, but that's going to require some calc)
600ft/117ft/s = 5.12s until the obstacle giving is a climb rate (50ft/5.12s) of about 9.77ft/s (~585fpm sounds about right, doesn't it?)
Even though we get a better climb performance at a lighter weight, as worst case I will use the 9.77 in the 2000lb calculation
Now at 2000lbs we need to accelerate from Vr to Vx and how long it takes to do that.
t = (105 - 80) / 5.76 - assume the acceleration remained constant after rotation
4.34s
Like the gross calculation we now cover an additional
d = vt + 1/2a*t^2
d = 80 * 4.34 + (5.76 * 4.34 * 4.34)/2
d = approximately 400'
560 + 400 = 960ft. Now lets use that vertical speed of 9.77ft/s to figure out how far to gain that 50' - it still takes 5.12s to climb the 50'
in that 5.12s we went
d = vt
d = 105 * 5.12
~540ft
560ft take off roll +
400ft acceleration to Vx +
540ft climb the last 50'
1500ft to climb the 50' obstacle.
Add a few % at the end for some rounding and call it 1600' to get over a 50' obstacle
I didn't double check math, so I'm sure I probably made a mistake in there and someone can go all Nelson Muntz on me.
Disclaimer: These numbers are pulled out of my ass, and not be to used for any sort of real world calculations and only an example of how *I* would do it.
Gross weight: 2400lbs
Takeoff roll: 800ft
Distance to clear 50': 2000'
Rotation speed: 60mph
Vx: 80mph
The above are at max gross.
Your current weight: 2000lbs
First convert to common units.
Vr: 88ft/s and
Vx ~117ft/s
The following variables and formulas are used
d = distance, v = velocity, t = time, a= acceleration, F = force m = mass (in this case we will use weight, I'm not going to use slugs)
v = at
F = ma
d = vt + 1/2at^2
We only know d and v at this point for gross weight.
But we can rearrange
v = at
so that
a = v/t and
d = vt so that
t = d/v and plug those into the d = vt +1/2at^2 formule and since we are starting from 0 we only need the 2nd half of the equation getting
d = vt/2 this can be rearranged so that
800 = 88 * t / 2
t = ~18.2 seconds
We can now determine acceleration
v = at
88 = a * 18.2
a = 4.8ft/s/s
And now what is the engine and prop doing for us:
F = ma
F = 2400 * 4.8
F = 11520lbf/s/s
Now use this to determine a at the new weight
11520 = 2000 lbs* a
a = 5.76ft/s/s
Now determine the Vspeed factor (this should have been taught somewhere before or during commercial)
sqrt(current wt/gross wt) = .91 call it .9 for ease of use and add a few % to your final numbers.
Vr = 80ft/s
Vx = 105ft/s
v = at
80 = 5.76 * t
t = 13.9 second
d = 1/2*at^2
d = 1/2*5.76*13.9*13.9
d = ~560ft
Even if we just want to use this without calculating the time to accelerate to Vx and doing calculus because of drag and all that stuff, the 50' distance is now down to 1760'
But, doing the rest of the math:
At gross it took us 6 seconds to accelerate to Vx (and lets assume we gain no vertical distance in that as a worst case)
In that 6 seconds at gross we covered another ~600ft. So we've used 800 (t/o roll) + 600ft leaving us 600' to climb 50' (it's less because we climbed during Vx, but that's going to require some calc)
600ft/117ft/s = 5.12s until the obstacle giving is a climb rate (50ft/5.12s) of about 9.77ft/s (~585fpm sounds about right, doesn't it?)
Even though we get a better climb performance at a lighter weight, as worst case I will use the 9.77 in the 2000lb calculation
Now at 2000lbs we need to accelerate from Vr to Vx and how long it takes to do that.
t = (105 - 80) / 5.76 - assume the acceleration remained constant after rotation
4.34s
Like the gross calculation we now cover an additional
d = vt + 1/2a*t^2
d = 80 * 4.34 + (5.76 * 4.34 * 4.34)/2
d = approximately 400'
560 + 400 = 960ft. Now lets use that vertical speed of 9.77ft/s to figure out how far to gain that 50' - it still takes 5.12s to climb the 50'
in that 5.12s we went
d = vt
d = 105 * 5.12
~540ft
560ft take off roll +
400ft acceleration to Vx +
540ft climb the last 50'
1500ft to climb the 50' obstacle.
Add a few % at the end for some rounding and call it 1600' to get over a 50' obstacle
I didn't double check math, so I'm sure I probably made a mistake in there and someone can go all Nelson Muntz on me.
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Bro do you even lift
someone's day at work is clearly slower than my day at work.
EdFred
Taxi to Parking
I took that into consideration, but at such low and close velocities (10%) found that it was OK to just go with m1 * a1 = m2 * a2
Took longer to explain it than do it. Doing it takes like 2 minutes.
The E 6 B does it in 15 seconds, and the DPE will trust the answer, but it will be very close to Ed's.
If the OP prints out Ed's calculations, and uses them for the DPE, he should pass that part of the test.
If the OP prints out Ed's calculations, and uses them for the DPE, he should pass that part of the test.
texasclouds
En-Route
Yea, that’s not fancy math at all. ;-)
texasclouds
En-Route
I don’t fudge factors, bruh!
EdFred
Taxi to Parking
It's not fancy it just really ends up being
d = vt/2 and
v = at
Everything else ends up cancelling out on both sides of the equation but someone wanted me to show my work.
Edit: it's actually even simpler than all that explanation.
WTnew * Vrnew^2
--------------------------- * Dgross = Dnew
WTgross * Vrgross^2
For the t/o roll at least.
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It's a shame that Piper didn't take the same approach to AFM/POH that Cessna did/does. The Cessna chapter on Performance (chp 5) include "fudge factors" for types of runway, altitude, temperature, flaps, and other conditions. Lots of performance data as well as ideas how to address different situations. I'm not saying the C172 manual should be used for the Arrow, but it will give you an idea how to adjust for performance.
MauleSkinner
Touchdown! Greaser!
Good thing the E6B will do it by itself, cause nobody’s showing anybody how to make the E6B do it.
I prefer walnuts in my fudge.
Arnold
Cleared for Takeoff
OP doesn't say which model PA-28R they are flying. I pulled out an old Arrow II (PA-28R-200) manual and it has a take off distance chart which should answer his questions. I don't have charts for the original 180 hp PA-28R. I would suggest OP first confirm that the documentation they have is complete.
I've previously mentioned Lady Luscombe's extensive documentation (all 8 pages of it). L8 manual says add 3% per 1000' altitude (I use density altitude but it does not say to do so) for the ground run on take off. Caution: It also says rate of climb is 800' / min. which is pure fiction.
HOWEVER, back to OP's issue.
Dear Mr. Examiner. The charts available to me have extremely limited information. Due to this I cannot confidently determine the actual take off distance given the conditions we are expecting. I can say the only numbers I am confident in indicate we do not have sufficient runway for the proposed operation. Therefore, we must meet at an airport with a runway which is at least "x,000" feet long. I respectfully suggest. JFK. Love, Applicant.
I've previously mentioned Lady Luscombe's extensive documentation (all 8 pages of it). L8 manual says add 3% per 1000' altitude (I use density altitude but it does not say to do so) for the ground run on take off. Caution: It also says rate of climb is 800' / min. which is pure fiction.
HOWEVER, back to OP's issue.
Dear Mr. Examiner. The charts available to me have extremely limited information. Due to this I cannot confidently determine the actual take off distance given the conditions we are expecting. I can say the only numbers I am confident in indicate we do not have sufficient runway for the proposed operation. Therefore, we must meet at an airport with a runway which is at least "x,000" feet long. I respectfully suggest. JFK. Love, Applicant.
Arnold
Cleared for Takeoff
For those who are interested the L8A (65 hp) take-off run is "625 feet hard turf surface." This does in fact seem to be about right.
The enhanced E6B app's that some of my partners had included takeoff and climb corrections, thus including the DENALT function in one electronic device. Thus, if you are using the electronic E6B, the function should be in it.
The first calculator that I mentioned was the takeoff and climb calculator from the Airforce, smaller than the E6B, also from that same WW 2 pilot. I had forgotten that I used the little one for takeoff calcs, and miss remembered using the E6B for that. Trying to remember the steps brought me to the realization that my memory was fuzzy.
Both computers have been in the College Park Air Museum for more than a decade. I should go over there and borrow them for an hour or two and refresh my skills.
The DENALT wheel calculated the ROC and TAKEOFF DISTANCE correction from altitude and temperature. Move the temperature into the window, and read the takeoff factor from the performance window. Then multiply the sea level, standard temperature performance with the correction factor, and you have which ever information you need.
% rate of climb is the same, just in a different window.
The E6B calculated TAS, and from that allowed calculating distance per hour/minute, or from distance/time, the speed over ground.
Flame away, I made a mistake.
The first calculator that I mentioned was the takeoff and climb calculator from the Airforce, smaller than the E6B, also from that same WW 2 pilot. I had forgotten that I used the little one for takeoff calcs, and miss remembered using the E6B for that. Trying to remember the steps brought me to the realization that my memory was fuzzy.
Both computers have been in the College Park Air Museum for more than a decade. I should go over there and borrow them for an hour or two and refresh my skills.
The DENALT wheel calculated the ROC and TAKEOFF DISTANCE correction from altitude and temperature. Move the temperature into the window, and read the takeoff factor from the performance window. Then multiply the sea level, standard temperature performance with the correction factor, and you have which ever information you need.
% rate of climb is the same, just in a different window.
The E6B calculated TAS, and from that allowed calculating distance per hour/minute, or from distance/time, the speed over ground.
Flame away, I made a mistake.
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MauleSkinner
Touchdown! Greaser!
LOL…
Keep in mind that the OP’s problem is reducing weight, not DENALT.
(DENALT corrections can also be made pretty easily with a Koch Chart.)
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No, the first integral of acceleration is velocity. The first derivative of acceleration is called “jerk.”
Edited - Looks like someone beat me to it!
I truly did not expect this to become such a popular discussion. I appreciate everyone's responses!
Arnold's approach is the most appealing to me. It is undeniable, safe, and simple. Explaining to a DPE the extremely limited information in the AFM and the impact that has on my decision making I feel is appropriate.
I am not saying that the math doesn't work. However, I do not feel as if I am capable of confidently showing a DPE in a checkride scenario the (complex-ish) math without making an error. Admittedly, all this talk about a 9th grader being able to do this math makes me a little self-conscious
. As a junior in College (deans list so far), that math seemed beyond me.User Dwayne had made a reply not to far before this, utilizing very rudimentary math. He used the percentage bellow MGW and applied that percentage to the only available takeoff chart (MGW). This seems to me like "gues-timating"
But on that note, let's say the DPE accepts my answer of either waiting for better conditions or moving the aircraft. The DPE then proceeds to ask, "Well, how do you know that me and you are safe to fly later today on the flight portion?" Going by my logic of only using available data, my answer would be simple... we cant. However, we can...
The airport is 2500 feet long with 50 foot obstacles both directions. The airport is at sea level, however with forecasted temperatures, density altitude will be around ~1400 ft. With just me and a CFI (or DPE), the aircraft is beyond capable of taking off safely. With full fuel and two adult men, the aircraft will weigh 2282, 368 pounds under max gross. The aircraft will then be only 86% of its max gross weight. At MGW, at 1400 ft density altitude, the PA-28R-200 will require 1900 ft of runway. 86% of 1900 ft is 1634 ft. With a 1.5 margin, the aircraft will require 2451 feet (safely).
Is this flawed? I feel it would behoove me not to bring up unknown numbers.
PA28R is completely capable. The issue is proving performance with a lack of information. I could look at the DPE and say, "I've done it before and it worked out". I do not believe the response from my DPE would be pleasant.