Da Vinci and the 50/70 Rule
The aviation community is not immune from the laws of propaganda. Repeat something often enough and pilots will believe it, whether it’s true or not. Take, for example, the aviation enthusiasts who reverently cite Leonardo da Vinci to express their love of flying: “Once you have tasted flight, you will forever walk the earth with your eyes turned skyward, for there you have been, and there you will always long to return.” It’s a magnificent quote. You can find it in books, on websites, on posters at flight schools, and on all manner of pilot merchandise and gifts.
There’s one problem: da Vinci never said it. As Dave English demonstrates in his well-researched article, those words appear nowhere in da Vinci’s writings. See “The Famous Quote that da Vinci Never Said,” Air Facts Journal, Aug. 11, 2020. Rather, American television writer John Secondari penned those words in 1965 as part of a voiceover for a documentary he produced on Leonardo da Vinci. Alas, it’d be a much cooler quote if da Vinci had said it. But facts are facts.
Leonardo da Vinci
Mis-attributing an inspirational quote isn’t cause for alarm. But what about mis-quoting an aviation rule of thumb designed to help you determine whether your plane is operating safely enough to launch into the wild blue yonder?
Take the “50/70 Rule” (a.k.a. the 70/50 Rule). Aviation gurus, from flight instructors to designated pilot examiners to flight school publications, constantly recite the 50/70 Rule as follows: “If you haven't reached 70% of your takeoff speed by the time you've reached 50% of the length of the runway, you should abort your takeoff." That’s verbatim from Boldmethod, a popular flight school educator. Others repeat the rule the same way, including articles on AvWeb, numerous flight schools, and even instructional YouTube videos. Long-time instructor and EAA Sport Magazine columnist Steve Krog discusses the rule with that identical verbiage in his March 2023 “Classic Instructor” column. And last month, AOPA’s Catharine Cavagnaro dedicated her “Flying Smart” column in AOPA Pilot’s June 2023 issue to questioning the efficacy of the 50/70 Rule, citing this same version of the rule: “If the airplane has not reached 70 percent of its rotation speed by the time 50 percent of the runway has been used, abort the takeoff.” These writers are not aviation lightweights: I think Krog’s and Cavagnaro’s columns are some of the best aviation content there is, and they’re typically the first articles I read each month in their respective magazines. Boldmethod’s content is also routinely useful.
But they all mis-cite the 50/70 Rule in a meaningful way. The 50/70 Rule is NOT about the length of the runway on which you happen to be idling, waiting for takeoff. It’s about whether your plane is performing properly such that you should take off. Specifically, it’s about whether your plane’s performance matches roughly what you’ve calculated will be your takeoff roll.
Accordingly, here’s the correct 50/70 Rule: "If on your takeoff run you haven't achieved 70% of your rotation speed by the time you're 50% down your CALCULATED TAKEOFF DISTANCE, abort your takeoff."
You don’t have to take my word for it that that’s the proper rule of thumb: the FAA routinely recites this version of the rule in its training materials. Here are two recently published FAA Safety Briefings that do so, Aircraft Performance and Calculations and Pattern Precision. The FAA also repeats the proper version of the rule in its recent Safety Briefing entitled “10 Tips for Safer Takeoffs and Landings” on its “Cleared for Takeoff” channel on Medium.com.
So, why is the difference between the two versions of the rule meaningful? First, it’s important to understand where the 50 and the 70 come from: basic physics. For uniformly accelerated motion, distance varies directly with the square of the takeoff velocity. For a comprehensive discussion of the underlying formula and these principles, I recommend Aeronautics for Naval Aviators, pages 182-192. But the short version for our purposes is simple: 70% of rotation speed requires (70%)² of the takeoff roll, or 49% of the takeoff roll. That’s not 50%, but this is, after all, a rule of thumb. (Being an imprecise rule of thumb also allows the 50/70 Rule to ignore the fact that propeller planes do not actually exhibit uniform acceleration, as Figure 2.32 from Aeronautics for Naval Aviators, below, reflects).
With that in mind, it’s easy to see why the popular version of the rule isn’t that helpful: a plane that accelerates to 70% of its rotation speed by the runway’s halfway point will, all other things being equal, achieve its rotation speed as it rolls over literally the last inches of the runway. Yes, a rule of thumb that helps you lift off just before hitting the grass might be helpful at some level, but it’s certainly not ideal, or even safe.
An exaggerated example helps demonstrate why reference to the runway length should be all but irrelevant. Imagine I'm taking off in my Bonanza from Denver’s Runway 16R, length 16,000'. I'm light, and I calculate my takeoff roll at, say, 1500', with a rotation speed of 80kts. Using the widespread but incorrect version of the 50/70 Rule, if I haven't reached 70% of my rotation speed (56kts) by the time I'm 50% down the runway (8000'), I should abort my takeoff. Using this version of the rule, I will (ridiculously) roll more than 5 times my expected takeoff distance before I consider aborting! Goodness, if I haven’t accelerated to 56kts by the time I’m even 10% down that runway — in this case 1600’, more than my entire expected takeoff roll — something is wildly wrong with my airplane, my takeoff calculations, or both.
Using the correct version of the 50/70 Rule resolves these problems. First, hopefully no one will attempt takeoff on a runway shorter than their calculated takeoff roll (plus a safety margin, described below). Second, using the example above, if I haven’t achieved 70% of my rotation speed (again, 56kts) by the time I’m halfway down my calculated takeoff roll (in this case 50% = 750’), I’ll know that my plane isn’t performing consistent with basic physics, and I should figure out why before further attempting to launch skyward.
A caveat: strict adherence to the (correct) 50/70 Rule will likely result in unnecessarily aborted takeoffs, because real world takeoff rolls rarely achieve those of the test pilot and new airplane that established the performance charts. As a result, to make use of the 50/70 Rule in the real world, we should apply a healthy margin to our expected takeoff distance. (That additional margin can also account for a propeller plane’s lack of constant thrust, as well as the increase in drag and decrease in rolling friction as the plane accelerates. See Figure 2.32).
How much margin? That will depend on your equipment, technique, and risk tolerance. Perhaps the best way to find the right margin is to compare your actual takeoff rolls to those predicted by your performance charts. If for any given set of conditions, your takeoff roll is typically 10% more than the performance chart predicts, add a 10% margin. In that case, you’ll have your own, useful 55/70 Rule. (Of course, if your typical takeoff rolls are considerably longer than your performance chart predicts, it might be worth having an instructor review your technique, or a mechanic inspect your powerplant).
With this tweak, the 50/70 Rule provides a useful tool that has a good chance of alerting us to a takeoff anomaly early enough to deal with it safely on the ground.
A sketch from da Vinci’s Codex on the Flight of Birds illustrating his Grande Nibbio flying machine
Da Vinci lived by a motto: ostinato rigore, or stubborn rigor. If we apply such rigor to our analysis of our flying, we’ll do more than repeat rules of thumb, checklists, and the like. We’ll dig into them, understand them, and thereby continually refine our methods and techniques to be safer and more confident pilots.
“Man, when he has great wings attached to him, by exerting his strength against the resistance of air and conquering it, is enabled to subdue it and raise himself up on it.”
