Top of climb calculation?

Ben2k9

Ben2k9

Pre-takeoff checklist
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Ben2k9
Ok I have my plane climbing at about 520fpm with Vy @ 78kias. I’m trying to figure out distance travelled to get to cruising altitude and I’m not sure if the way I’m doing it is correct. So I’m just taking the 520fpm rate and multiplying that times the altitude climb, and coming up with a time, and then multiplying time x speed to get distance (forget about wind for now). So for 6000 feet of climbing that’s 11.5 minutes, and 11.5 minutes x 78kts is 15nm.

This is simple enough, but wouldn’t the airspeed be happening at a diagonal angle, therefore not covering the full 15nm? Am I overthinking this and doing it right or is there a more precise formula one would use to calculate this?
 
Seems you would need to know your ground speed not your indicated speed.


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I just use the charts in the POH, those do a good job, that's what the examiners like to see, and is what the engineers who designed the plane factored in.

*notice the lines are not perfectly linear, so they already factor various atmospheric and other factors as you climb. Below is just an example for a Piper POH.. if you are unfamiliar with how to read this then the POH has some examples, or your CFI would be happy to review it with you

upload_2018-7-1_15-17-0.png
 
Ben2k9 said:
So I’m just taking the 520fpm rate and multiplying that times the altitude climb, and coming up with a time, and then multiplying time x speed to get distance (forget about wind for now)
Click to expand...
Keep in mind that your climb performance will degrade as you ascend and the air gets thinner, at the same time your TAS and IAS will also begin to differ as well. That's why in the chart I posted above the lines are not straight, they taper off as you go up in altitude, etc.

In your example, to climb from sea level to 6,000 ft, per the chart above that would take you about 1-2 gallons of fuel, take about 12 minutes, and cover about 16nm. If you were to climb twice as high, say to 12,000 ft, then notice that your time to climb end up 34 minutes, but your distance goes all the way up to 54 nm... the time almost triples, and the distance almost quadruples.. this shows how well the graph already factor in several components to account for the performance of the plane as it ascends and the atmospheric conditions change

So unfortunately, it is not as simple as just taking the sea level fpm climb and doing some algebra with your airspeed.. much more complex, but good news is that the engineers already did the hard work for you!


PS - for small altitude changes your approach will work fine. For instance, if you are trying to manage your vertical speed on a localizer or rnav approach to hit your step downs, then it is pretty easy to say "alright, I need to lose 1,000 ft, GPS says I'll be there in two minutes, so lets aim for 500 fpm descent"
 
Follow Tantalum's advice. There is nothing in the Airman Certification Standard about calculating TOC. In my opinion it is a waste of brain cells: Your goal in flight planning (aside from staying on course) is to determine if you will have enough fuel on board to complete the flight plus reserves, and you do this by picking out checkpoints/fixes, measuring the distance between them, and then applying ESTIMATED winds aloft to calculate ESTIMATED groundspeed. Once you are in the air, all bets are off because the actual winds will not be even close to what you got when you checked the winds aloft. If you insist on calculating TOC and include that information in calculating your ESTIMATED time of arrival at your destination, any error in TOC calculation will be eclipsed by changes in enroute groundspeed due to ACTUAL winds.

I do not know where you get your winds aloft information from; the FB (winds and temperatures aloft) requires interpolation and to be even close to "correct" you must fly over the reporting point at the even-thousand-foot altitude (the FB does not contemplate density altitude) in the FB at its valid time. Fat chance. Even the Skew-T winds are based on forecast models, not measurements. Garbage in, garbage out.

Bob
 
Like Bob said, don’t get too wrapped around the axle on this for accuracy.

To do the calculation if you’re studying for a written question you need two things. Rate of climb, and groundspeed.

Use rate of climb to get a TIME to climb to your new altitude.

Use groundspeed (which has to include winds, so for planning purposes all you can do is a no-wind or estimated wind number) to calculate DISTANCE using the time from above.

All of this above is complicated by the fact that most trainers can’t maintain a climb rate as they go up, as evidenced by this chart from a 172 manual. As someone else mentioned, use the aircraft chart if it has one when talking about TOC or TOD with an examiner. And then be prepared to discuss errors that can be introduced by changes in that “garbage in” number, as Bob put it.

Or put more simply... Is this airplane really climbing to book values today? Can I really hold a perfect Vy throughout the climb? Etc.

He real world is this: Be conservative. What you’re really looking at climb home for is where you’ll be changing to cruise power and for a way to calculate fuel burn for the flight since you’re covering less ground during the climb. If you’re going to error, assume the climb will be slower and longer than it will be, for fuel calculations in the real world.

A controller may step climb you (causes a HUGE difference in fuel burn in a turbine aircraft for example, if you get stuck at a lower altitude for a while before cleared up to final cruising altitude), a cloud might be in your way, blah blah blah. Always assume the worst in fuel planning and keep some extra gas on board for “mom and the kids” when you can.
 
Oops. Forgot the 172 chart page. Here it is. Look at climb rate as you go up.

ecc6a226f81bac9197bd01ea0c58ac37.png
 
bobmrg said:
Follow Tantalum's advice. There is nothing in the Airman Certification Standard about calculating TOC. In my opinion it is a waste of brain cells: Your goal in flight planning (aside from staying on course) is to determine if you will have enough fuel on board to complete the flight plus reserves, and you do this by picking out checkpoints/fixes, measuring the distance between them, and then applying ESTIMATED winds aloft to calculate ESTIMATED groundspeed. Once you are in the air, all bets are off because the actual winds will not be even close to what you got when you checked the winds aloft. If you insist on calculating TOC and include that information in calculating your ESTIMATED time of arrival at your destination, any error in TOC calculation will be eclipsed by changes in enroute groundspeed due to ACTUAL winds.

I do not know where you get your winds aloft information from; the FB (winds and temperatures aloft) requires interpolation and to be even close to "correct" you must fly over the reporting point at the even-thousand-foot altitude (the FB does not contemplate density altitude) in the FB at its valid time. Fat chance. Even the Skew-T winds are based on forecast models, not measurements. Garbage in, garbage out.

Bob
Click to expand...
I would agree with all of the above except the statement that its a waste of brain cells for two reasons:

1. It's always good to be familiar with what's in your AFM/POH/whatever. If you start saying this page isn't necessary, where do you stop? I guess I'm just morally opposed to ignoring anything in the airplane's documentation, especially when it's tied to a statement that "there is nothing in the [ACS]". ;)

2. Even if you use estimates/rules of thumb/experience as a (valid) replacement for the climb data, as you also noted, the same errors will apply to the rest of the flight. These errors will apply to the climb segment no matter what method you use. Applying the same logic (admittedly to a rare unlikely conclusion), it would seem that any preflight planning is a waste of time, and all you need to do is get airborne and then determine whether you have enough fuel for the trip. Admittedly a very low percentage of flights are fuel critical, but when you get to the point of actually planning a fuel-critical leg, having a knowlege of how realistic your charts are makes a huge difference.
 
denverpilot said:
Like Bob said, don’t get too wrapped around the axle on this for accuracy.

To do the calculation if you’re studying for a written question you need two things. Rate of climb, and groundspeed.

Use rate of climb to get a TIME to climb to your new altitude.

Use groundspeed (which has to include winds, so for planning purposes all you can do is a no-wind or estimated wind number) to calculate DISTANCE using the time from above.

All of this above is complicated by the fact that most trainers can’t maintain a climb rate as they go up, as evidenced by this chart from a 172 manual. As someone else mentioned, use the aircraft chart if it has one when talking about TOC or TOD with an examiner. And then be prepared to discuss errors that can be introduced by changes in that “garbage in” number, as Bob put it.

Or put more simply... Is this airplane really climbing to book values today? Can I really hold a perfect Vy throughout the climb? Etc.

He real world is this: Be conservative. What you’re really looking at climb home for is where you’ll be changing to cruise power and for a way to calculate fuel burn for the flight since you’re covering less ground during the climb. If you’re going to error, assume the climb will be slower and longer than it will be, for fuel calculations in the real world.

A controller may step climb you (causes a HUGE difference in fuel burn in a turbine aircraft for example, if you get stuck at a lower altitude for a while before cleared up to final cruising altitude), a cloud might be in your way, blah blah blah. Always assume the worst in fuel planning and keep some extra gas on board for “mom and the kids” when you can.
Click to expand...

"To do the calculation if you’re studying for a written question"

No guarantee that ASA or anyone in the industry has all of the test questions, but their test prep book does not include any questions on TOC.

Bob
 
Rate of climb is linear or pretty close to it for an airplane with a normally aspirated engine. If you know your ROC at departure and cruise altitude you can average them to get your average ROC. Then you can find your time to climb. Once you know that you can find your distance. This would be for an airplane that doesn't already have a time, fuel, and distance to climb table.

Keep in mind that even if the winds aloft forecast was entirely accurate, you're going to be climbing so will encounter differing winds... taking that into account and all the other factors that are going to be changing or not accurate in the first place, at some point trying to get a precise calculation becomes an exercise in futility.

Also most people aren't going to want to climb at Vy on a cross country and most manufacturers don't give the numbers for a cruise climb, despite most of them recommending such a climb for better forward speed, visibility, and engine cooling. Expect about 20% more time and 40% more distance for a cruise climb.
 
Tantalum said:
I just use the charts in the POH, those do a good job, that's what the examiners like to see, and is what the engineers who designed the plane factored in.

*notice the lines are not perfectly linear, so they already factor various atmospheric and other factors as you climb. Below is just an example for a Piper POH.. if you are unfamiliar with how to read this then the POH has some examples, or your CFI would be happy to review it with you

View attachment 64546
Click to expand...

This Piper chart you show seems deficient.
Where's the adjusted performance lines for single wing operations? ;)
 
Ben2k9 said:
Ok I have my plane climbing at about 520fpm with Vy @ 78kias. I’m trying to figure out distance travelled to get to cruising altitude and I’m not sure if the way I’m doing it is correct. So I’m just taking the 520fpm rate and multiplying that times the altitude climb, and coming up with a time, and then multiplying time x speed to get distance (forget about wind for now). So for 6000 feet of climbing that’s 11.5 minutes, and 11.5 minutes x 78kts is 15nm.

This is simple enough, but wouldn’t the airspeed be happening at a diagonal angle, therefore not covering the full 15nm? Am I overthinking this and doing it right or is there a more precise formula one would use to calculate this?
Click to expand...

If you are just looking for a simple method, what you are doing works. Just include a TOC check point to determine accuracy of your estimate.
 
The POH or performance supplement for my plane doesn’t have that exact data (like denverpilot and tantalum showed). It just shows the CAS airspeed for Vx and Vy for various flap settings. I’m not worried about a written exam, just have checkride in a week and trying to get all my knowledge squared away. Wasn’t sure if this would come up
 
Ben2k9 said:
The POH or performance supplement for my plane doesn’t have that exact data (like denverpilot and tantalum showed). It just shows the CAS airspeed for Vx and Vy for various flap settings. I’m not worried about a written exam, just have checkride in a week and trying to get all my knowledge squared away. Wasn’t sure if this would come up
Click to expand...

Read the ACS...that is the examiner's guide on areas to cover during the oral.

Bob
 
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