Descent Below VASI on Approach

[jynxyjoe]

The problem with such analyses is that you have to make assumptions before you can calculate anything. Based purely on the assumptions you make above, and further assuming that when you say “same point”, you mean only the distance along the ground rather than flare height, the following analysis applies.

The distance covered during the flare is

flare distance = Radius of loop * sin(approach angle).
​

The circle in question is the imaginary loop the pilot is performing during the pullup from an angle of descent to level flight. For instance, during a pullup from a 3 degree angle of descent, aircraft's flies 3 degrees of some circle as it changes to a landing attitude, and the portion of the circle looks like a slice of pie.

The radius of the loop is determined by the load factor and velocity of the aircraft. If you assume a constant load factor and velocity, the radius is constant and the above equation shows that the flare distance increases with an increasing approach angle.

That doesn't mean that a steeper angle always results in a longer total landing distance, because there are other variables at play, such as how many g's the pilot is willing to pull during the flare and how willing he is to change his airspeed based on his approach angle. And, there's no reason to think that 3 degrees provides the shortest distance; that angle is probably more geared towards a safe approach rather than a short landing.

My bet for the shortest landing would be a steep approach followed by a higher-than-normal load factor flare. The reasoning is that the loop you're going to fly has a smaller radius with more g's and you can go from your steep angle to level flight in a shorter horizontal distance. You probably wouldn't bleed off much airspeed in the flare so your touchdown might be a bit fast, but a slightly slower approach speed would fix that. Regardless, brakes are more effective than aerodynamic drag.


(The source for the above analysis is "Aircraft Performance and Design", by John D. Anderson. However, the conclusions are mine.)

Dr. John Eckalbar (PHD) says that it doesn't matter at all about the steepness of the approach. At least that's how I read it in "flying high performance singles and twins". He says any thought of a shorter landing distance as resultant of a steeper approach is the result of an imagined vector.

 

[tgrayson]

Dr. John Eckalbar (PHD) says that it doesn't matter at all about the steepness of the approach. At least that's how I read it in "flying high performance singles and twins". He says any thought of a shorter landing distance as resultant of a steeper approach is the result of an imagined vector.

I'll have to look and see what his assumptions are. The mathematics in all the aircraft performance books take into account the approach angle.

 

[tgrayson]

Dr. John Eckalbar (PHD)

Looks like I only have his Bonanza book.

(BTW, Eckalbar is a PHD in Economics. Still, he gets his theory righter than any other pilot that I've seen.)

 

[400A]

It doesn't make scientific sense at all. In fact if one flares high, regardless of angle, at the same speed they flare low they will likely land sooner because they won't have ground effect issues and will burn speed faster. Can someone break the science down as to how approach path can lengthen ones landing distance? If 3 aircraft approach the same point, one at 1 degree, one at 3 degrees and one at 5 degrees, each with the exact same weight, exact same conditions/configuration, and each at the same speed which will land shortest/longest and why?

I am not saying this is wrong, I don't know. The current conclusion proposed by 400A and agreed by mini is that the lower, 1 degree and higher, 5 degrees will all have a longer landing distance due to the flare with the steeper approach and some horizontal thing I am confused about making the shallower approach longer. I would expect each the distance to be shorter with a steeper glide angle, but only marginally.

Reference what Tgrayson posted. We are starting to get off the track and into the performance engineering side of things and theoretical speak.

IF, and that is one whopper of an IF. A pilot can fly at a 5 or 6 degree slope (so now your descent rate is double what it would be on a 3 degree slope), and can time the flare correctly, induce enough G load and lift to arrest to the descent, and put the airplane down on the same point as a 3 degree slope and flare, then yes, your landing distance will be shorter. Consider though, at 100 knots and no wind, that would be almost 1000 FPM descent or roughly 10 knots of downward velocity.

I want to stress, this isn't some holier than though uber pilot speak. I in no way claim to make perfect approaches and landings every time BUUUUT, I don't justify flying illegally into runways that are too short via the regs, because I can "put the airplane down on the numbers" or "fly in steeper" to get a shorter landing distance. The regs and the AFM/POH have a set way that landing distance is calculated and what I am allowed to do with those calculated numbers. These rules are, in affect, there to protect the public and property and while a "normal" approach path may not be the absolute shortest distance and airplane will land in, it is, IMO, the best balance of performance and repeatability by the average pilot without requiring special skill or abnomal manuevering.

Tell you what, to quote Days of Thunder, if you can, next time you are flying with a student or by yourself, find an adequetly long runway. Compute your max performance landing numbers and fly by the book and see how they compare. Then try to beat that performance (total runway used for landing, not just ground roll). Report back on how you did it, how difficult it was and how "controlled" it really felt. Give me an honest run, and I bet I'll beat you.

 

[shdw]

400A: The whole point of what I did here was to show that this:

Too shallow increases ground roll and too steep increases ground roll, relative to your computed numbers from the POH dependant on how the POH numbers were derived.

I'm starting to think that no one teaches this to primary students.

is an erroneous belief unsupported by the physics behind how an aircraft flies. As tgray pointed out the glide path has little to do with the landing distance or ground roll. That was the point I was trying to make, I am not claiming one to be shorter than the other. Sure the math behind it might leave one slightly shorter than another but that is negligible, and teaching a student that 3 degrees is a magic number for the shortest landing distance or ground roll is an unsupported claim, a wives tail.

IF, and that is one whopper of an IF. A pilot can fly at a 5 or 6 degree slope

This is not a big if at all, at best glide speed in a 172, book published of 9 to 1 you are on a 6.4 degree glide path. With other calculations from other sites saying you can get 12 to 1 that is a 4.8 degree glide path. A 1500 RPM approach at 60 knots in a 172 with 30 degrees flaps is about a 6 degree glide path or about 630 FPM descent, not an uncommon setting used in a 172.

I took the liberty of going through the amplified procedures of a few POH's I have handy, here is what is mentioned:

172R: "...at 62 KIAS with 30 flaps using enough power to control the glide path."

Seminole: "...flown down final with full flaps at 75 KIAS..."

Arrow: "...full flaps and enough power to maintain the desired airspeed and approach flight path."

You will note, non of these speak of the standard 3 degree glide path and in the arrow they even go as far as using the word "desired."


Now you mention 100 knots, take note that most small singles short field approach speed will be closer to 60 or at least in the 60's. To give a number to this, at 60 knots forward speed a descent of 530 FPM yields a glide path of 5 degrees. A 3 degree glide path at 60 knots is 320 FPM, quite a bit of power would be needed to achieve this with 30 degrees flaps as I am sure you know, about 1800 RPM.

The purpose of a steeper approach path on a short field approach is for obstacle clearance, if there were no obstacles than this wouldn't matter. If you have 100 foot trees and then a 2000' opening to land on a 3 degree glide slope won't be very helpful. Flying a steeper glide slope in that case would put you with more runway in front of you to work with when you were ready to flare. Without crunching the numbers I would guess around 200-300 feet of extra runway from a 6 degree as apposed to a 3 degree approach path. If you want the numbers crunched for this to see how drastically different they are let me know, I will gladly do that for you.

Compute your max performance landing numbers and fly by the book and see how they compare. Then try to beat that performance (total runway used for landing, not just ground roll). Report back on how you did it, how difficult it was and how "controlled" it really felt. Give me an honest run, and I bet I'll beat you.

I have done this, cut the landing distances in the book by about 20-30 percent. It was with an instructor who was briefed to make airspeed callouts every few seconds and go around would happen if we got less that 5 knots above stall. We flew the approach in a 172 at 40 knots, it was after I read about mushing it in at stall speed in the book stick and rudder. Obviously it is less safe, requires extremely good control, and is unnecessary for 99.99 percent of runways in the country.

As I mentioned in my first reply to this, landing distance is a direct function of the approach speed used, not descent path flown. The book values are based on the books published approach speed, fly slower and you will land shorter. Obviously this has a factor of safety involved as the slower you go the closer you are to stall and eventual pilot skill will not be sufficient. Ask I think it is pprogramer about this, flying at stall speed into runways for minimum landing distance.

 

[ppragman]

400A: The whole point of what I did here was to show that this:



is an erroneous belief unsupported by the physics behind how an aircraft flies. As tgray pointed out the glide path has little to do with the landing distance or ground roll. That was the point I was trying to make, I am not claiming one to be shorter than the other. Sure the math behind it might leave one slightly shorter than another but that is negligible, and teaching a student that 3 degrees is a magic number for the shortest landing distance or ground roll is an unsupported claim, a wives tail.




This is not a big if at all, at best glide speed in a 172, book published of 9 to 1 you are on a 6.4 degree glide path. With other calculations from other sites saying you can get 12 to 1 that is a 4.8 degree glide path. A 1500 RPM approach at 60 knots in a 172 with 30 degrees flaps is about a 6 degree glide path or about 630 FPM descent, not an uncommon setting used in a 172.

I took the liberty of going through the amplified procedures of a few POH's I have handy, here is what is mentioned:

172R: "...at 62 KIAS with 30 flaps using enough power to control the glide path."

Seminole: "...flown down final with full flaps at 75 KIAS..."

Arrow: "...full flaps and enough power to maintain the desired airspeed and approach flight path."

You will note, non of these speak of the standard 3 degree glide path and in the arrow they even go as far as using the word "desired."


Now you mention 100 knots, take note that most small singles short field approach speed will be closer to 60 or at least in the 60's. To give a number to this, at 60 knots forward speed a descent of 530 FPM yields a glide path of 5 degrees. A 3 degree glide path at 60 knots is 320 FPM, quite a bit of power you will need to achieve this with 30 knots flaps as I am sure you know, about 1800 RPM.

The purpose of a steeper approach path on a short field approach is for obstacle clearance, if there were no obstacles than this wouldn't matter. If you have 100 foot trees and then a 2000' opening to land on a 3 degree glide slope won't be very helpful. Flying a steeper glide slope in that case would put you with more runway in front of you to work with when you were ready to flare. Without crunching the numbers I would guess around 200-300 feet of extra runway from a 6 degree as apposed to a 3 degree approach path. If you want the numbers crunched for this to see how drastically different they are let me know, I will gladly do that for you.





I have done this, cut the landing distances in the book by about 20-30 percent. It was with an instructor who was briefed to make airspeed callouts every few seconds and go around would happen if we got less that 5 knots above stall. We flew the approach in a 172 at 40 knots, it was after I read about mushing it in at stall speed in the book stick and rudder. Obviously it is less safe, requires extremely good control, and is unnecessary for 99.99 percent of runways in the country.

As I mentioned in my first reply to this, landing distance is a direct function of the approach speed used, not descent path flown. The book values are based on the books published approach speed, fly slower and you will land shorter. Obviously this has a factor of safety involved as the slower you go the closer you are to stall and eventual pilot skill will not be sufficient. Ask I think it is pprogramer about this, flying at stall speed into runways for minimum landing distance.

Energy in vs. energy out. If you fly slower you're ground roll will be less. That's why bushrats sometimes drag it in. A better approach is to come in steep right above stall and then use ground effect to flare even further reducing your airspeed before touchdown.

For the best control with the shortest distances, I've noticed for me anyway that shallow (approximately 2* or less over the numbers) with power, full flaps, and right above stall gives me the shortest field performance (you transition to the slow speed farther out, you don't fly a stabilized approach at 1.05Vso all the way down).

Straight up the best short field performance is steeper. The slower you come in at a steep deck angle the more energy you're going to bleed off as you use ground effect to flare. The problem is keeping from getting too fast as you come in (which is easy to do at such steep angles). Another problem is making sure you have sufficient speed to flare while you're in ground effect to begin with, otherwise you'll clonk the nose wheel on hard, or hit the prop. That's why I like the first method.