5 hours ago, Doug47 said:

Not correct. There’s no way a 737-700 at MTOW takes off at much less than what’s quoted by offical Boeing sources. 
 

154,500 lbs. 26k. Optimum flap settings. 5200ft. 
There’s no way at well over the MTOW, and zero flap will it use less (LCY airport). 
 

Sorry, but either MSFS or PMDG or both have it wrong. No surprise as it’s a game. 
 

 

But again, this data doesn't mean what you're trying to make it mean. 

You aren't using ground roll data (which is what the original question references - whether an aircraft with both engines operating can get off the ground at City.)

You're using normal takeoff data.  This data assumes an engine failure one second prior to V1, and a subsequent continuance of the takeoff with greater than 50% performance loss, AND ability to complete the climb while clearing all second-segment obstacles by a given margin.  That second-segment climb obstacle clearance requirement is why this data is so much longer than if an engine doesn't fail, despite what was stated above - it requires a significantly longer time on the ground, accelerating more slowly before liftoff, to go off in the energy state required to clear these obstacles with severely reduced performance.

 If you were only using ground roll data, then yes an engine failure a couple seconds prior to rotation wouldn't make an enormous difference. But when you factor in the second segment climb requirement, it certainly does.  Take a look at the large difference between normal takeoff distance data vs min ground roll data, you'll see what I mean. 

As stated above, this back of the napkin math is interesting but really not much better than guessing. There are just far too many factors here that aren't being accounted for.  If we had an actual performance engineer working with actual Boeing data this would be doable, but...

... and BTW, Boeing DOES have this data, contrary to an above claim. Now whether it was gathered directly in flight test vs extrapolated from the thousands of data fields that are collected on each test flight, I do not know. But I do know that we had a crew do a very dumb thing years ago, involving flaps on takeoff. Part of their "recalibration" involved analysis of the data needed here, which we requested and received from the Boeing performance engineers.  It validated to be fairly accurate in the level D sim as well. 

3 hours ago, Stearmandriver said:

But again, this data doesn't mean what you're trying to make it mean. 

You aren't using ground roll data (which is what the original question references - whether an aircraft with both engines operating can get off the ground at City.)

You're using normal takeoff data.  This data assumes an engine failure one second prior to V1, and a subsequent continuance of the takeoff with greater than 50% performance loss, AND ability to complete the climb while clearing all second-segment obstacles by a given margin.  That second-segment climb obstacle clearance requirement is why this data is so much longer than if an engine doesn't fail, despite what was stated above - it requires a significantly longer time on the ground, accelerating more slowly before liftoff, to go off in the energy state required to clear these obstacles with severely reduced performance.

 

Out of curiosity, how much runway do you think a 737-700 uses at max weight and with 24k engines? 

The "normal takeoff data" you are referring to does not include any obstacle clearance considerations. That would have to be done on a runway by runway basis. It does include consideration of 1st and 2nd segment climb gradient requirements. These are minimum climb gradients (not having anything to do with obstacles) that must be obtainable in these segments with one engine inoperative. For a twin, that would be positive first segment gradient (which is not usually limiting) and a 2.4% second segment gradient.

I'll repeat what I said before and clarify for you. Boeing does not conduct specific flaps up takeoff testing, which would include Vmu tests, rapid rotations, etc. They would not be able to produce the "normal takeoff data" for approval of flaps up takeoff operations. There is enough data to go back and make some reasonably good estimates, basically using much more refined versions of the "back of the envelope" calculations that have been presented here. (BTW, I am an actual former Boeing performance engineer.)

It's a good thing their analysis matched your level D sim since it's from much of the same data.  It doesn't mean that any takeoffs were actually conducted in a real airplane with flaps up.

Edited May 17, 20224 yr by Donstim

So… what is the consensus here? Take off performance is realistic or not? By the way I‘ve found Topcat to be really limiting with the 737-700. Taking off at Bogota at 20 degrees celsius Topcat basically said I am only allowed to take on board 15 passengers and no baggage. I ignored it, loaded 128 pax and some cargo, uprated to 26k and took off not even needing half the runway available. So it‘s either Topcat being wrong or indeed the performance on the 737 in MSFS is too good.

On 5/16/2022 at 7:59 AM, Donstim said:

An interesting exercise, 😀. But, since you invited anyone to comment on errors in your back of the envelope calculation...

Yes, we have a scrum-like approach here (iterative and agile teamwork).... 🙂

Slowly we are narrowing down on the mechanisms and physical factors, which should be considered for an accurate calculation. So let me go another round, which includes our newest learnings (from your and @martinboehme 's post):

On 5/16/2022 at 7:59 AM, Donstim said:

It decreases with increasing airspeed, so assuming a constant thrust at the rated static thrust level is optimistic.  A fall off of about 20% between 0 and 160 knots would be in the range I would expect to see.

Correct, considering thrust reduction makes sense, so my newest version of the spreadsheet includes that. 20% less at Vr might be a bit pessimistic (Bjorn has it at -19% at V2), but lets use a -20% reduction at 85m/s to be on the safe side.

On 5/16/2022 at 7:59 AM, Donstim said:

It is difficult to know what an appropriate flaps up lift coefficient would be since there may be tail clearance issues in trying to achieve the CLmax determined for the airplane with flaps up. In other words, you may not be able to achieve the angle-of-attack to reach CLmax. Your assumed CL may be okay, or it may not be. 

The airfoil link has all the relevant diagrams. CLMax of 1.6 is achieved at AoA of 15° which is matching the geometry limitation according to martinboehme's input. 

We should also understand, that the closest thing to what the OP did in real world would be a VMU test (at low T/W ratio). It is totally different to a normal take off, so looking at offical tables is useless.

For VMU additional factors, which "help" taking off early are:
- Ground effect
- Drag reduction due to ground effect

I guess, we can ignore them but keep in mind, that these are factors, which make the calculation pessimistic.

15 hours ago, martinboehme said:

This is the drag at the speed achieved at the end of the runway. I assume you're simply conservatively applying this drag from the start of the takeoff run?

It looks as if this is just the drag produced by the wing though -- not the rest of the airframe?

Good points about the drag! Here my remarks:

In my spreadsheet I properly modelled the increasing drag every 2.5m/s speed increment.

But - and there is a big but - as you correctly point out, it is only about wing drag, but no parasitic drag and no lift drag.

So true drag in theory could be higher due to these two additional components (and some others, albeit small ones), but there are also reasons why my calculation is pessimistic:
- The Cd at CLmax is not valid for the whole take off. In fact, it only has impact during rotation, when AoA is raising. At AoA=0 (for 97% of the take off run), Cd is close to zero, looking at the diagrams in the link 0.01 to be precise.
- Same for induced drag (= lift drag). As CL only becomes effective during rotation, induced drag stays close to zero for the largest portion of the take off run.

So what is the true drag for a 737-700 during take off? Take a look here (arent we lucky that the guy used a 737-700 for his study?).

Overall (and very comprehensive) Cd is 0.0355. So a bit less than the 0.04 I used. So, fine, that means that my initial spreadsheet was even a bit too pessimistic, but in the version below I have corrected that.

15 hours ago, martinboehme said:

By the way, going back and looking again at the numbers I used, I noticed that the 89 kN correspond to 20,000 lbf thrust. It looks as if the -700 typically uses the 24k engines, so that could at least partially compensate for the various effects I've neglected.

Another crucial point. The 737-700 is even available with the CFM56-7B26 engine, having 26,300 lbf (117 kN) thrust. This considerably improves the picture.

After all these factors are considered (and adding a bit safety margin by going to 1.5 for CLmax) my new spreadsheet is this:

737TakeOff.xlsx

Changes to the spreadsheet:
- Thrust is steadily reduced over the take off run, reaching -20% at the VLO.
- Drag is calculated based on Cd=0.0355 for every speed increment
- Static thrust corrected for the CFM56-7B26 engine

Conclusion:

Basically the same as before! 🙂 With the changed factors, making the initial assumptions partly too optimistic and partly too pessimistic, we can reliably conclude now that the 737-700 can take off at 82.5m/s after 1383m with the specified weight.

Btw., in case you haven't noticed, you can see the formulas I used if you click on a cell in the spreadsheet...

17 hours ago, Doug47 said:

Not correct. There’s no way a 737-700 at MTOW takes off at much less than what’s quoted by offical Boeing sources. 
 

154,500 lbs. 26k. Optimum flap settings. 5200ft. 
There’s no way at well over the MTOW, and zero flap will it use less (LCY airport). 
 

Sorry, but either MSFS or PMDG or both have it wrong. No surprise as it’s a game. 

It is not a game. You are wrong. The error of the latest calculation is too small that you could be right. You are also fixated wrongly on Boeings manuals for pilots. You would have to review the test data for Boeings Vmu tests at MTOW (which is not public) to compare with this sim excercise.

In the end, physics is very honest. You consider the relevant factors, put in the numbers and get a result, to which the real 737 obeys with sufficiantly small error margins. Missing factors with my current calculation are only tire friction and ground effect, one making the result optimistic and the other making it pessimistic, in the end both about canceling out each other.

Again, everybody is invited to substantiate my calculation more... 🙂

Edited May 17, 20224 yr by mrueedi

4 hours ago, Donstim said:

BTW, I am an actual former Boeing performance engineer.

🙏

Then I hope you're suitably entertained by my amateurish fumblings here! 😉 (Intentionally speaking only for myself.)

On a more serious note, I'm very much aware that I'm taking time out from pretending to be an airline pilot so I can pretend to be a performance engineer. My goal with both of these is to challenge myself and learn -- and thanks to the input from people such as yourself and @Stearmandriver I'm doing just that!

5 hours ago, Donstim said:

The "normal takeoff data" you are referring to does not include any obstacle clearance considerations. That would have to be done on a runway by runway basis. It does include consideration of 1st and 2nd segment climb gradient requirements. These are minimum climb gradients (not having anything to do with obstacles) that must be obtainable in these segments with one engine inoperative. For a twin, that would be positive first segment gradient (which is not usually limiting) and a 2.4% second segment gradient.

I'll repeat what I said before and clarify for you. Boeing does not conduct specific flaps up takeoff testing, which would include Vmu tests, rapid rotations, etc. They would not be able to produce the "normal takeoff data" for approval of flaps up takeoff operations. There is enough data to go back and make some reasonably good estimates, basically using much more refined versions of the "back of the envelope" calculations that have been presented here. (BTW, I am an actual former Boeing performance engineer.)

It's a good thing their analysis matched your level D sim since it's from much of the same data.  It doesn't mean that any takeoffs were actually conducted in a real airplane with flaps up.

The climb gradient requirements are what I was referencing, since any approved runway isn't going to have obstacles piercing these gradients in the departure corridor (or it's going to have a turn procedure published).  These climb gradient requirements significantly lengthen the minimum ground roll data, which is what we'd need but don't have here. 

I also never said that Boeing conducted flaps up takeoff testing.  I said they have the data necessary to make these calculations, while those of us here do not. 

On the one hand you seem to be wanting to argue with me, but that's odd because you end up agreeing with me ;).

 

 

8 hours ago, Doug47 said:

Out of curiosity, how much runway do you think a 737-700 uses at max weight and with 24k engines? 

My very rough guess, based on flying the plane for years but not based on any calculations, would have been right around 5,000ft for min ground roll all-engine.  That's why I don't think that the fact the PMDG was able to do this indicates any sort of dramatic flight model problem. Does it mean you'd try it in a real airplane, based on a guess? Of course not. 

6 hours ago, Stearmandriver said:

My very rough guess, based on flying the plane for years but not based on any calculations, would have been right around 5,000ft for min ground roll all-engine.  That's why I don't think that the fact the PMDG was able to do this indicates any sort of dramatic flight model problem. Does it mean you'd try it in a real airplane, based on a guess? Of course not. 

I’m super confused. Because didn’t you say it would be a LOT less then what I quoted (5200 ft)?  
 

The point being which that illustrates, is the take off run would by extended with zero flap, and at a weight ‘well over mtow’ by some margin. 

Well, actual ground run would, if your goal was just min ground run (which is how I'm understanding the original question, but maybe I've got that wrong?)  But we never use min ground run, so in the case of normal takeoff data that assumes the engine failure and subsequent climb gradient, yes,  5,200 feet sounds good to me. 

Sorry if I misunderstood something. 

One more round with the math as defined in the first book mentioned under "which is the best book to study ... aircraft performance": ‘Introduction to FLight’ by John D Anderson.

Fortunately, this book is online available as pdf, so please download from here and go with me to page 522, chapter 6.15 Take off performance. 

Anderson's extensive mathematical derivation concludes in these formulas:

When applying this formula for the 737-700, based on Anderson's sample calculation for the CJ1 on page 527, I get a Slo (lift off distance) of:

1446m ✔️

This result is reasonably close to my own calculation in the spreadsheet before. And it still means, that there was more runway at the end of the OPs take off...

To the doubters, I really suggest to come up with some solid substance when trying disprove this and my earlier calculation. Just saying, "yeah, but the Boeing manuals say otherwise" (for normal operations) is not sufficient imho. This is not gut feeling, this is solid math, incorporating all sensible factors. A level of math fidelity, which I can not imagine that PMDG or any other dev surpasses when building their addons.

 

 

 

Edited May 19, 20224 yr by mrueedi