kuffel(at)cyberport.net
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 Posted: Fri Oct 19, 2007 4:13 pm Post subject: Determining Vx & Vy |
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Warning: Long & SemiTechnical
Thom Riddle's approximation method for determining critical climb
and other speeds will certainly get you "good enough" close. But
since we have to test fly 40 hours on our homebuilts anyway, why
not use that time to get exact data.
First, Thom's approximate method works best starting from true
airspeeds at sea level for Vh (high/maximum cruse) and Vs1 (clean
stall). Then the obtained estimates for various V speeds needs
to be converted back to indicated. Thus we want accurate
conversions from indicated to true airspeeds.
To get this you need three things: 1) some graph paper, 2) any
GPS, even a Wally World $100 special, and 3) an Excel spreadsheet
from me (email me directly for a copy: kuffel(at)cyberport.net ).
The spreadsheet asks you to fly a box of 4 different stable
tracks at a constant indicated airspeed (noting the resulting GPS
ground speeds) for each data point. Only 3 legs are required for
this calculation but the fourth leg gives you redundant results
to judge the quality of each data point.
Now at no greater than 1000 foot intervals determine the true
airspeed throughout your available indicated airspeed range at,
say, 5 knot (or mph) intervals. Density altitude is best but
this can be determined from indicated altitude, temperature and
pressure on your E6-B circular slide rule. (And you thought you
wouldn't need it after completing your training.)
[Of course, don't gather data at the low end of your range below
2000 feet above ground level, particularly until you have
thoroughly investigated the stall characteristics for your aircraft.]
Now draw some graphs. For each indicated airspeed plot density
altitude vs true airspeed. Extend these graphs to sea level to
get a set of sea level points of TAS vs IAS. From these graphs
(or density altitude data) plot a true airspeed vs indicated
airspeed conversion for regularly spaced density altitudes,
extending the graph moderately for airspeeds you were not able to
fly.
Now determine the indicated airspeeds for maximum cruse and clean
stall at several altitudes. Interpolating as needed, graph your
TAS vs altitude for Vh and Vs1. Extend these two graphs to sea
level to use with Thom's approximations. Having determined your
critical V speeds at TAS use your sea level graph to determine
the equivalent indicated V speeds.
But wait, there's more. Having done this much work, you might as
well measure your critical Vx and Vy directly. For each of a
series of altitudes do a series of saw tooth flights at, again
say, 5 knot/mph increments. Climb from 500 feet below the target
altitude to 500 feet above the target maintaining a constant
indicated airspeed. Measure the time from 250 feet below to 250
feet above. The shorter measurement interval is to help insure
your climb rate is stabilized. Now at idle, glide back down
measuring the time from 250 above to 250 below.
Vy (best rate) is simplest. Plot the rate of climb vs indicated
airspeed at each altitude. Draw a smooth curve through the
points. Where the curve peaks is the indicated airspeed for best
rate of climb at that altitude. Your Vy should decrease with
altitude until it meets the Vx you determine below at the
aircraft's maximum altitude.
For Vx (best angle) we need to convert our IAS and rate of climb
to TAS and climb. The TAS and rate of climb form the hypotenuse
and vertical leg of a right triangle. Divide the rate of climb
(in feet/min) by the TAS (in knots/mph) to get an arbitrary
number proportional to the sine of your angle of climb. Plot the
arbitrary unit points against their original *indicated*
airspeed. Draw a curve through these points. The peak of this
curve is the *indicated* Vx for this altitude. This number
should remain fairly constant with altitude. If not, something
is wrong.
If you want to know the actual angle of climb for Vx at various
altitudes convert to identical units. First indicated Vx to TAS
for an altitude. Then TAS(knots) * 101.2 = TAS(feet/min) or
TAS(mph) * 88 = TAS(feet/min). Divide TAS(ft/min) by rate of
climb (ft/min) to get the actual sine of your climb angle. Use
excel or your high school Trigonometry book to get the equivalent
angle for your computed sine value.
If you want your best glide speed, do the exercise in the two
prior paragraphs on your decent data. Look for the IAS at the
minimum of the sine data curve. The actual decent angle gives
you AGL to landing range. While the glide speed obtained will
not be exactly correct for the engine-out/prop-stopped condition,
it will be closer than your ability to hold an exact airspeed if
you are facing that situation. (As they say, ask me how I know.)
While you are doing this, get some IAS vs power settings at
various altitudes as well as gas consumptions at different power
settings/altitudes. If you don't have a fuel flow meter,
take-off, climb, descend and land on one tank; cruse for 1/2 or
one hour on another; see what it takes to refill the "cruse" and
the up/down tank. Now you can compute accurate range data for
that altitude/IAS including climb/decent consumption.
This may seem like a lot of graphing but when you are done the
test period will have gone by a lot faster. And you will be the
proud possessor of more accurate data about your aircraft's
performance than the vast majority of pilots know about the plane
they are flying. It also makes is a lot easier to justify the
log book entry you have to make at the end of the test period
about the aircraft being safe to fly if anyone chalenges the
statement. It might even be worth your while to do this testing
on your favorite spam can or purchased experimental.
If you have questions about the above or other aircraft
performance data collection please contact me or your local EAA
Flight Advisor (list at eaa.org ). Unlike some gummint agencies
we really are here to help and the test period accident rate for
people using Flight Advisor services has been ten times lower
than those who didn't.
Tom Kuffel, CFI
Whitefish, MT
EAA Flight Advisor
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