# Is there a method for calculating change in V-speeds with a change in weight for a Cessna 172?

For example, what would the rotation speed (Vr) and stall speed (Vs) be at maximum takeoff weight versus flying with a single occupant? (2297 lb vs 1807 lb)

Instead of doing detailed calculations like you were in a jet, there is a useful rule of thumb advocated by author/instructor William Kurshner for working that out, which while not exact down to a fraction of a knot, is conservative and easy to do and is therefore perfect for regular GA flying.

Reduce Vs/Vr by half of the percentage of the weight reduction. So if stall speed is 50kt at gross, and the weight reduction from 2297 to 1807lb is about 21%, and half of that we can round up to about 11%, your stall speed is going to be about 45 kt at that weight.

So if I was using say, 55kt as a rotation speed at gross (I seem to remember that's what it was on the 172), I'd use about 49 kt at 1807 lb. Close enough for 99.9999999999% of normal operation in a Chevy Biscayne Of The Air like the 172.

• wouldn't half the percentage be 45 kt, starting from 50? So instead of 55 my preferred rotation speed would be 49 kt. Commented Oct 21, 2019 at 20:02
• Oops... mental fart. I thought my resulting number seemed low, but didn't think it through. Thanks Commented Oct 21, 2019 at 21:08
• Could also look in the Pilot Operator Handbook (or Manual) for the plane in question. There are charts showing things like takeoff distance at various weights & temperatures. aeroatlanta.com/docs/aero-atlanta-c172sp-poh.pdf I think you want section 5. Commented Oct 21, 2019 at 22:12
• Yeah but much of the time the handbook isn't available. My homebuilt has no manual at all... I just play it by ear. I don't even look at the airspeed on takeoff, and go by feel and instinct, until I accelerate to climb speed. Commented Oct 22, 2019 at 0:06
• POH or equivalent should be in the plane. Recall ARROW is acronym for required items (USA): (A)—Airworthiness certificate FAA Form 8100-2, Standard AirworthinessCertificate, or FAA Form 8130-7, Special Airworthiness Certificate (as applicable) (R) Registration certificate FAA Form 8050-3 (R)—Radio station license FCC Form 605 (O)—Operating limitations FAA-approved Airplane Flight Manual (AFM) and/or Pilot’s Operating Handbook (POH), and/or limitations attached to FAA Form 8130-7 (W)—Weight and balance Documentation provided by aircraft manufacturer, maintenance and modification records Commented Oct 22, 2019 at 11:47

The THEORETICAL way to calculate reduction in stall speed is to take the listed stall speed for 2297 lbs and apply math as follows:

square root (1807 lbs/2297 lbs) x 50 knots. Comes out pretty close to what John K says.

The SAFE way is to take your plane about 3000 feet AGL in the flap configuration you choose and actually do it, making sure your eyes in your plane at your weight gives your actual stall speed on your airspeed indicator. 172s are very forgiving, just make sure CG is right and stay on the rudder; do these all day long, power on AND power off.

As far as reduction in rotation speed, this may have an application for an emergency backwoods muddy field takeoff, but little else. The "trike" gear is designed to keep the plane below the AOA needed to fly until you rotate. In addition to being safer, it also shortens takeoff roll by reducing drag.

Rotating at a lower speed increases risk of a freak gust lifting and slamming the plane back down, and lowers safety margins should cross winds require any type of aileron or rudder input. It is especially a bad idea in higher performance aircraft, where an uncontrollable torque roll may develop. It might be best, especially on a windy day, to stick with 55 knot rotation speed. It is a good habit to be in.

There is no such thing as "Vr" in a Cessna 172. The concept of Vr belongs ONLY in jets. In a Cessna, you fly the airplane off when it's ready, and you do that by feel, not by numbers.

• Having done both private and professional flying in the 172, I will say that’s incorrect and in fact the 172 DOES have a Vr associated with the takeoff roll, albeit the value is generally affixed to a single number, depending on the takeoff being executed. Commented Oct 22, 2019 at 8:28