Flare Height Adjustment in the E175
Introduction
Was your first landing in Denver or Salt Lake a bit firmer than you were planning it to be? Density, weight, and winds all affect our closure rate with the ground, and hence the point at which we need to start flaring in order to arrive at the pavement at around 100 FPM if we want to keep a consistent flare load factor (i.e. “same pull on the yoke”). Glide path angle likewise changes sink rate as well as flare geometry, so I’ll address those in a separate article. Let’s look at some relationships that affect flare timing, then make some rules that we can employ on the go so that we can more consistently land the airplane under a variety of conditions.
The math
A higher vertical speed will mean a quadratic change in flare radius.
Radius of turn or flight path change scales with v^2 for a given load factor. If we want to keep load factor roughly constant in the flare independent of density or winds to avoid getting too close to α-max (or simply to do the same thing consistently), then we need to make a quadratic distance change for a linear speed change:
∆h(f)=∆v^2, where h(f) is flare height
If we’ve geometrically fixed our GPA to 3 degrees, then ∆h can be a function of either ground speed (GS) or vertical speed (VS). What’s important to keep in mind is that approach and ref speeds will not scale linearly with VS, because those are in KIAS, not KTAS, so you end up with density correction issues. To keep it simple, let’s use VS as our v unit and see what we end up with:
∆h(f)=∆VS^2
Let’s start with the base case that we used in the E175 flare geometry article. Assume a 130 knot Vref in no wind and a 25-foot flare height. On a 3-degree GPA, we get 130 nm/hr * 6076 ft / 60 min * tan (3) = 690 FPM. If we know the flare height should scale as the square of the speed, we just plug those numbers in:
h(f) = 25 = k * (690^2), where k is a constant that we need to apply.
Rearranging that gives us k = 19041. Punching in any arbitrary VS gives us this:
h(f)=VS^2/19041
Plotting some common values gives us a familiar-looking parabola:
∆h(f)=∆v^2, where h(f) is flare height
If we’ve geometrically fixed our GPA to 3 degrees, then ∆h can be a function of either ground speed (GS) or vertical speed (VS). What’s important to keep in mind is that approach and ref speeds will not scale linearly with VS, because those are in KIAS, not KTAS, so you end up with density correction issues. To keep it simple, let’s use VS as our v unit and see what we end up with:
∆h(f)=∆VS^2
Let’s start with the base case that we used in the E175 flare geometry article. Assume a 130 knot Vref in no wind and a 25-foot flare height. On a 3-degree GPA, we get 130 nm/hr * 6076 ft / 60 min * tan (3) = 690 FPM. If we know the flare height should scale as the square of the speed, we just plug those numbers in:
h(f) = 25 = k * (690^2), where k is a constant that we need to apply.
Rearranging that gives us k = 19041. Punching in any arbitrary VS gives us this:
h(f)=VS^2/19041
Plotting some common values gives us a familiar-looking parabola:
Higher sink rates require increasingly higher flare initiation.
Worth noting is that it starts to get steep after 1000 FPM, which is probably why they want us to avoid that region. Now we can create a table using the FPM and flare cutoffs as inputs and use the same calculations as earlier to find new flare cutoffs, touchdown spots, and secondary aimpoints:
Table: flare geometry calculations for a variety of expected sink rates.
Higher sink rates mean earlier flare cutoffs and later touchdowns.
The fractional numbers in those last three rows of the table are chunks of 200 feet that start at the base of stripe 1 and assume 120-foot stripes and 80-foot gaps. Thus “stripe 1.6” is the back end of the physical stripe and “stripe 1.8” is halfway through the gap from stripe 1 to stripe 2.
Diagram showing fractional stripe counting.
Three conclusions emerge:
- The higher the VS, the further back our cutoff stripe goes. At 850 FPM, we need to start our flare when we start eating up stripe 1. Values of 0-1 mean runway numbers, and negative numbers mean piano keys, depending on how the numbering is set up.
- As we flare from a greater height, we necessarily chew up more of the touchdown zone, so our touchdown stripe goes further downrange. At 1000 FPM we’re on stripe 7, or the beginning of the 1500-footers. If we’re intent on landing closer to stripe 4, then we’d need to accept some combination of a higher touchdown sink rate or flare later with a higher α and load factor.
- If touchdown FPM is held constant at 100, then the greater ground speed means we have a shallower touchdown angle and consequently need to look further down the runway in the flare.
Load factor Implications
If we feed the above inputs into our flare geometry model and calculate flare arcs accordingly, we end up with the following data set:
Table: Load factor and flare geometry for a variety of sink rates.
As expected, the arc radii, TC, get larger the faster our sink rate gets. As posited earlier, they should scale quadratically with sink rate. We already calculated flare height, h(f), as a quadratic function of sink rate, so h(f) and TC should have a linear relationship. If we divide TC/h(f), we end up with a set of values that are all within 2% of one another in the orange rows. One final sanity check we can do is to calculate the load factor, which is just 1 G plus the centripetal acceleration, Ac=v^2/r. To get that, we convert GS and TC into meters, then we derive Ac in meters/second squared as the acceleration value. Dividing by the gravitational constant, 9.8 m/sec^2, gives us G. Adding that to our baseline 1 G gives us a pretty consistent 1.08 G across the orange row at the bottom. Looks like it works.
On-the-fly Adjustments
Now that we’ve done the hard work, let’s turn it into some simple rules. I’m not going to sit there on final thinking “Hmm, 800 squared divided by 19 grand…” and I’d be impressed if you could do it. If we look at a table of VS and cutoff stripes, some simple rules jump out:
Table: differences in flare geometries per 50 FPM.
- For every 100 FPM, start flaring VS/100 feet earlier (e.g. 7 feet earlier going 700->800 FPM).
- For every 100 FPM, start your flare half a stripe earlier.
- For every 100 FPM, look two stripes deeper downrange.
- For every 100 FPM, you will touch down about 2/3 of a stripe later.
Density Corrections
We know from Density for Dummies that we get 3% ∆ρ for every 1000 feet or per every 10 degrees and 1.5% ∆TAS. If TAS and VS scale linearly, we can apply that same multiplication factor. If we start with a baseline of 700 FPM, then a 1.5% difference works out to 10 FPM. In other words:
For every 1000 feet in altitude, we gain 10 FPM VS.
For every 10 degrees C we gain 10 FPM VS.
Denver (5400 MSL) on a hot (35 C) day? 5.4 thousand plus 20 degrees over T0 gives us 54 + 20 = 74 FPM, so flare about half a stripe, or 7ish feet earlier. You should also adjust how far out you configure.
Wind Correction
If we get a 10-knot headwind or tailwind on a 130-knot speed, that works out to 10/130 = 7.7%. 7.7% of 700 FPM is 54 FPM, which is close to 50.
Rule: start your flare a quarter stripe earlier/later for each 10 knots tail/headwind. Be sure to consider approach speed additives and when you remove them.
Conclusions
If you want to get a consistent touchdown at 100 FPM under a variety of density conditions with a consistent load factor, plan your flare cutoffs earlier and look further down the runway in your flare. If you constrain TCH=50, 3 degrees, and load factor, that will mean a slightly later touchdown point with higher approach sink rates. If you absolutely need to hit a spot from a higher sink rate, then you will need to relax at least one of those constraints and have more precise timing. For example, 1.08 G only uses up about a quarter of your green-dot load factor, so that’s an area to look into. Please get in touch with any suggestions, or if you’d like to collaborate on solving this for your aircraft type.