Calculating E175 Flare geometry
Understanding exactly when to flare based on visual cues is an essential part of the Jacobson Flare cutoff technique. The basic idea is to start with a primary aimpoint and a lookdown cutoff. When the cutoff goes under the glareshield, you initiate your flare. The major advantage of this technique is that longitudinal references are more consistently precise than vertical ones due to our shallow approach angles. On a 3-degree glide path, the 60:1 rule tells us that we go about 3 units vertically for 60 units laterally, or 1 foot for every 20. This means that if we use a longitudinal reference to start our flare, and are off by 20 feet longitudinally, we are only off vertically by 1 foot. In other words, the use of longitudinal flare cutoff gives us a 20:1 magnification of precision, usually much better than eyeballing it.
My variation on the Jacobson Flare technique is what I call the intermediate and secondary aimpoint (ISAP) technique: look at a primary aimpoint until the flare cutoff, then systematically walk my eyes up through a series of intermediate aimpoints to a secondary aimpoint during the flare. This has a few advantages:
Everything below is specific to landing the E175 and its geometry, though much of the theory likely applies to other types. To get started, we need to know a few things:
My variation on the Jacobson Flare technique is what I call the intermediate and secondary aimpoint (ISAP) technique: look at a primary aimpoint until the flare cutoff, then systematically walk my eyes up through a series of intermediate aimpoints to a secondary aimpoint during the flare. This has a few advantages:
- By keeping your eyes at a slight nose-down, it reduces the tendency to float.
- If you subscribe to the idea that "the plane follows the eyeballs" then you can use the intermediate points to gauge float/sink and make small corrections all the way down.
- Runway upslope and downslope effects get dampened due to your intermediate and secondary aimpoints being sloped up or down as well.
- Reduction in the tendency to float with approach speed additives (e.g. gust or SPIS) due to faster recognition of over-flaring.
Everything below is specific to landing the E175 and its geometry, though much of the theory likely applies to other types. To get started, we need to know a few things:
- How high our eyeballs are in the aircraft.
- Where our eyeballs are relative to the gear on approach and landing.
- How to find the flare cutoff angle out the front and the resulting distances and visuals to expect.
A note on seat position
Seating position is crucial if you plan to use the flare cutoff technique. I wondered why my flare was inconsistent for a while until I understood and fixed the issue that I had. If you’re a pilot of average height, you should be able to line your eyeballs up with the alignment balls under the windshield center post and see down the glareshield to the windshield heating elements. If you’re over 6 foot, you will likely have to scoot back, which will obscure your view of the heating element and make it harder to judge your flare cutoff. The solution I’ve adopted is scooting my chair so that my eyeballs are in the same angled line with the glareshield, which puts them behind and above the three alignment balls. Bottom line: if you can’t see the heater element, adjust until you can.
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Note: several numbers are rounded in the narrative for brevity. The original values were not rounded, so following along you may see slight discrepancies if you reproduce this using rounded inputs, especially for trigonometric functions with small angles.
In the E175 you want to start your flare at about 25 feet under ISA SL conditions. To find where everything else is, let’s open the E175 APM: from Figure 2.2 we get 8’6” to GSD (C) and Figure 2.7 door height 4’5.5”. That door is in line with the top of the flight deck windows, so we get a height of ~13 feet, then subtract half a foot for our eyeball displacement below that for an eyeball height of 12.5 feet (Q1, green arrow in sketch). Comparing the wheelbase versus eyeball base leg arrows on the sketch gets us 41.7 feet ahead of the mains (Q2a, red arrow). Our friend Pythagoras gives us the distance from eyeball to main gear as sqrt(12.5^2+41.7^2) = 43.5’ (purple arrow). The angle of our head to the gear is atan(12.5/41.7)=16.7 degrees. This will be useful to find our eyeball height at different pitch angles, where it rotates around that purple arc. The E175 sits slightly nose-up on the ground (.6 degrees), so we’ll need to back that out when doing calculations. At zero pitch (θ) we’ll have 16.7-.6=16.1 degrees baseline eyeball angle. Thus, our eyeball height above the wheels (He) as a function of θ will be He=sin(16.1+θ)*43.5 and the length ahead will be L=cos(16.1+θ)*43.5 (Q2b).
In the E175 you want to start your flare at about 25 feet under ISA SL conditions. To find where everything else is, let’s open the E175 APM: from Figure 2.2 we get 8’6” to GSD (C) and Figure 2.7 door height 4’5.5”. That door is in line with the top of the flight deck windows, so we get a height of ~13 feet, then subtract half a foot for our eyeball displacement below that for an eyeball height of 12.5 feet (Q1, green arrow in sketch). Comparing the wheelbase versus eyeball base leg arrows on the sketch gets us 41.7 feet ahead of the mains (Q2a, red arrow). Our friend Pythagoras gives us the distance from eyeball to main gear as sqrt(12.5^2+41.7^2) = 43.5’ (purple arrow). The angle of our head to the gear is atan(12.5/41.7)=16.7 degrees. This will be useful to find our eyeball height at different pitch angles, where it rotates around that purple arc. The E175 sits slightly nose-up on the ground (.6 degrees), so we’ll need to back that out when doing calculations. At zero pitch (θ) we’ll have 16.7-.6=16.1 degrees baseline eyeball angle. Thus, our eyeball height above the wheels (He) as a function of θ will be He=sin(16.1+θ)*43.5 and the length ahead will be L=cos(16.1+θ)*43.5 (Q2b).
Now that we know our eyeball height, distance from mains, and how it relates to pitch, we need to determine our lookdown cutoff angle (light green line above) so that we can manipulate that. To do that, we need the following:
- Longitudinal visual reference outside the parked airplane.
- Distance of that reference from our eyeballs.
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With all of this information, we can now determine our visual flare cutoff. We know that we want to start flaring at 25 feet, so let’s do some trigonometry to figure out our flare cutoff. The below sketch illustrates a lot of these distances, though it is laterally compressed, so it looks a bit cartoonish:
With our gear at 25 feet (Hg) our eyeballs will be at He+Hg feet up. We know He=sin(16.1+θ)*43.5 and θ=3, so we end up with He=14.2, so our eyeball height is 39 feet from the ground. To get the lateral distance (De), we know it’s the height divided by the tangent of glide path angle. 39/tan(3)=749 feet back from aimpoint, and our mains are Dm=749+41=790 feet back. To get the cutoff distance (Dc), we know that cutoff angle is 13.2-θ, so at θ=3 we get 10.2 degrees. 39/tan(10.2)=218 feet ahead of our eyeballs. If our eyeballs are 749 feet back from the aimpoint and our cutoff is 218 feet ahead of our eyeballs, then the cutoff is 749-218=531 feet back from our aimpoint. If we use standard 120-foot centerline stripes with 80 foot gaps (total 200 feet per set), then 2 full stripes and gaps gets us 400 feet, plus a stripe gets us 520 feet. If our aimpoint is the far end of stripe 4, then our cutoff is almost exactly the start of stripe 2.
One thing to note in this illustration looking at the purple dashed lines is that the mains will touch pretty far behind you if you don’t flare. Plugging our numbers into Albright’s wonderfully-reasoned article tells us the mains will touch 14.2/tan(3)+41=313 feet behind your aimpoint in the E175.
We want to touch down with a sink rate of about 100 FPM. If we come in at a Vref of 130 knots, then our vertical speed on the descent is 130 nm/hr * (6076 ft/60 mins) * tan(3)=690 FPM. To find the flare time, we can assume an average of the two values of 690+100/2=395 FPM, or 6.6 FPS. From our 25-foot flare height, 6.6 FPS gives us 25 ft/6.6 FPS=3.8 seconds in the flare. Let’s call it 4 seconds in practice.
Let’s assume we don’t decelerate much during the flare. If we start with 130 knots, we’re doing 130 nm/hr * (6076 ft/3600 seconds)=219 FPS. That means we cover 219 FPS*3.8 sec=833 feet in the flare prior to touchdown. If our mains started out Dm=790 feet back from stripe 4, and they traveled 833 feet in the flare, then they’ll end up 833-790=43 feet past the aimpoint, right in the gap between stripes 4 and 5, still right inside the thousand-footers. Thus, a four-second flare from 25 feet will put you right on the 1000-footers in the E175.
Now that we have the distances sorted out, we need to determine our secondary aimpoint. We know that we want 100 FPM, or 1.66 FPS at touchdown. We also know that we’re doing 219 FPS forward, so our FPV at the moment of touchdown is atan(1.66/219)=.435 degrees. We know from experience that we end up with about a 5-degree pitch up, so when our mains touch our eyeballs are He=sin(16.1+5)*43.5=15.7 feet off the ground. Our secondary aimpoint is thus Dsa=15.7/tan(.435)=2062 feet downrange. This works out to stripe 15 or the end of the touchdown zone markings (unless it’s a short runway). At night on precision runways, you should look for the far end of the touchdown zone lights. Thus to land right on the 1000-footers, make a four-second flare as you progressively move your eyeballs up to the far end of the touchdown zone.
One thing to note in this illustration looking at the purple dashed lines is that the mains will touch pretty far behind you if you don’t flare. Plugging our numbers into Albright’s wonderfully-reasoned article tells us the mains will touch 14.2/tan(3)+41=313 feet behind your aimpoint in the E175.
We want to touch down with a sink rate of about 100 FPM. If we come in at a Vref of 130 knots, then our vertical speed on the descent is 130 nm/hr * (6076 ft/60 mins) * tan(3)=690 FPM. To find the flare time, we can assume an average of the two values of 690+100/2=395 FPM, or 6.6 FPS. From our 25-foot flare height, 6.6 FPS gives us 25 ft/6.6 FPS=3.8 seconds in the flare. Let’s call it 4 seconds in practice.
Let’s assume we don’t decelerate much during the flare. If we start with 130 knots, we’re doing 130 nm/hr * (6076 ft/3600 seconds)=219 FPS. That means we cover 219 FPS*3.8 sec=833 feet in the flare prior to touchdown. If our mains started out Dm=790 feet back from stripe 4, and they traveled 833 feet in the flare, then they’ll end up 833-790=43 feet past the aimpoint, right in the gap between stripes 4 and 5, still right inside the thousand-footers. Thus, a four-second flare from 25 feet will put you right on the 1000-footers in the E175.
Now that we have the distances sorted out, we need to determine our secondary aimpoint. We know that we want 100 FPM, or 1.66 FPS at touchdown. We also know that we’re doing 219 FPS forward, so our FPV at the moment of touchdown is atan(1.66/219)=.435 degrees. We know from experience that we end up with about a 5-degree pitch up, so when our mains touch our eyeballs are He=sin(16.1+5)*43.5=15.7 feet off the ground. Our secondary aimpoint is thus Dsa=15.7/tan(.435)=2062 feet downrange. This works out to stripe 15 or the end of the touchdown zone markings (unless it’s a short runway). At night on precision runways, you should look for the far end of the touchdown zone lights. Thus to land right on the 1000-footers, make a four-second flare as you progressively move your eyeballs up to the far end of the touchdown zone.
Finding intermediate aimpoints
In the Cessna 172 I used the ISAT technique of counting up the stripes past the cutoff, roughly one per second, until reaching the secondary aimpoint. To find these intermediate aimpoints for the E175, we need to find intermediate positions in our flare and the eyeball FPV associated with them. Let's say that we continue downhill at a 3-degree GPA until we reach our 25-foot flare point, then join an arc on the red circle that intersects the runway at a .435-degree angle as we derived earlier. To find points along this arc, we need to find the center of the circle, C. We can draw the triangle CTF to figure this out and do some trig. Pythagoras tells us that the small base of that isosceles triangle, line TF, is sqrt(833^2+25^2)=833.7 feet. The swept angle TCF is just GPA-Flare=3.0-.435=2.565 degrees. If we chop triangle TCF into 2 right triangles CTM and CFM, we can find the coordinates for C. Length FM and TM is just 833.7/2=416.8, and angle TCM is TCF/2=1.282 degrees. TC=TM/sin(TCF)=416.8/sin(1.282)=18625 ft.
Now we can create a Cartesian coordinate model to find any point on the circle. We know that point C is 18625 feet above and slightly left of T, so we can find it by using sin(.435)*18625=141 ft for lateral and cos(.435)*18625=18624 ft for vertical displacement. If we set our touchdown spot T as 0,0, then the coordinates for C become -141, 18624. Plugging that into the equation for a circle, we can model any point along the arc as Distance=-141+sin(GPA)*18625 and Height=18624-cos(GPA*18625). A quick sanity check using GPA=3, our tangent line, spits out a distance of 833 ft and height of 25 ft, so the equations work.
If we plan to follow the flare arc for 3.8 seconds, then we traverse 2.565/3.8=.68 degrees/second. Using this information, we can sequence each second in our flare and the associated coordinates of the main wheels using the sin/cos calculations above. Next, we find where our eyeballs will be given a pitch angle the same way we did upthread (I guessed on the pitch, though it makes marginal difference), then using instantaneous FPV and eyeball height (using the above equations) we get Eye FPV distance = eyeball H/tan(FPV). Subtracting Eye FPV Distance from eyeball distance gives us the position of the FPV target from the touchdown spot. We already know that TD spot is 44 (or 43, rounding errors) feet past our initial aimpoint, so subtracting that out gets us the distance of AP2, AP3, AP4, and AP5 past the first one. If we start with stripe 4, that gives the last column as the stripe number to aim for each second.
If we plan to follow the flare arc for 3.8 seconds, then we traverse 2.565/3.8=.68 degrees/second. Using this information, we can sequence each second in our flare and the associated coordinates of the main wheels using the sin/cos calculations above. Next, we find where our eyeballs will be given a pitch angle the same way we did upthread (I guessed on the pitch, though it makes marginal difference), then using instantaneous FPV and eyeball height (using the above equations) we get Eye FPV distance = eyeball H/tan(FPV). Subtracting Eye FPV Distance from eyeball distance gives us the position of the FPV target from the touchdown spot. We already know that TD spot is 44 (or 43, rounding errors) feet past our initial aimpoint, so subtracting that out gets us the distance of AP2, AP3, AP4, and AP5 past the first one. If we start with stripe 4, that gives the last column as the stripe number to aim for each second.
It gets harder to count stripes when they get up there, so it's easier to use the distance table then look at runway markings and plan the following:
- Stay on profile with your eyeballs going for the top of stripe 4, wait until you start seeing stripe 2 go under the glareshield and heater element, then start flaring.
- Aim your eyeballs at the top of stripe 5 for one second and make that your new aimpoint.
- Aim your eyeballs at the base of stripe 7 or the 1500-footers for the second second.
- Aim your eyeballs at the middle of stripe 9 or the 2000-footers or for the third second.
- Aim your eyeballs at stripe 15 or the far end of the 3000-footers for the fourth second.
Generalizing for other airplanes
Everything you see here is set up for the E175, but a lot of it probably works for other types as well. In writing this article, I used what I could find in the APM and from my own observations and pictures. I created a spreadsheet with a bunch of variables that can easily be adapted to other types. Yellow cells are required inputs (Vref, eyeball height, eyeball distance from gear, pitch, etc.), the rest are the consequent output calculations. If you would like to adapt this for your own aircraft, please drop me a line and I can send you the template. As always, operate per your SOP and AFM.
