The flight
speed of the so-called "Slow-Fly" planes (the real ones, not those
Foam stuffs equipped with Speed 400 motors and 500 mAh cells, or
more, and which monopolise your gymnasium for hours or cut your plane
in slices unscrupulously...) can be measured quite easily with just a
rule and a stopwatch. Interesting aerodynamical data can then be
determined.
A first
flight test with the motor will give you an idea on the cruise speed.
Then, remove
the propeller and replace it with an lead of the same weight in order
to keep the balance and throw your model over you head with an
initial speed similar to the cruise speed and control it so it will
glide straight ahead with constant speed and slope. Ask a friend to
time the flight duration and measure the distance between the
launching and the landing points. Do that several times and take the
mean values. In this way, flight duration t (in seconds), distance d
and altitude loss h (in meters) can be determined.
Put the
propeller again, fully charge the battery and fly level and straight
(as much as possible) your model at cruise speed until the battery is
discharged. Note the total flight duration T (in seconds).
We can now
easily calculate:
- The ground
speed Vx = d / t in metre / second
- The sink rate
Vz = h / t en metre / second
- The glide
ratio f = d / h,
From this
data, we can determined:
- The minimum
power Pu (in Watts) needed for a level flight. This power is
equivalent to the power needed to compensate (per time unit) for the
loss of potential energy Ep of the plane (Ep = m * g * h). So, we
have :
Pu = m * g*
h / t or Pu = m * g * Vz where m is the model's mass (in kilogrammes)
and g the gravitational acceleration (9,81).
- The thrust
force Fp (in Newton) for a level flight (at constant speed). As a
matter of fact, the energy of this force is W = Fp * d that is to say
per time unit, W / t = Fp * d / t = Fp * Vx = Pu = m * g * Vz or:
Fp = m * g *
Vz / Vx or Fp = m * g * h / d or Fp = m * g / f
- The overall
efficiency of the model (Needed power / Consumed Power) :
R = Pu / Pe
= (m * g * Vz) / (U * C / T) where U is the battery's voltage in Volt
and C the battery's capacity in Ampere-second.
In the case
of the "Magicien d'Oz" (data given by J.M.
Piednoir), we have:
- Flight
duration T with 3 x 50 mAh cells : 14 minutes or 840 seconds,
- Total masse :
31 grams,
- Glide duration
over 13 metres and from an altitude of 1,8 metres : 5,5 seconds.
Therefore we
have:
- Ground
speed : Vx = 13 / 5.5 = 2,36 m/s (or 8,5 km/h),
- Sink rate : Vz
= 1.8 / 5.5 = 0,327 m/s
- Glide ratio :
f = 13 / 1,8 = 7,22
- Level thrust :
Fp = 31 / 7, 22 = 4,29 grams
- Required power
: Pu = 0,030 * 9,81 * 1,8 / 5,5 = 0,0995 W
- Electrical
power : Pe = 3,45 * 0,050 * 60 * 60 / (14 * 60) = 0,77 W
- Overall
efficiency : R = 0,0995 / 0,77 = 12,9 %
Assuming the
motor efficiency is 45 %, the efficiency of the frame plus the
propeller is 12,9 / 0,45 = 29 %. If we suppose the propeller
efficiency is 55 %, then the efficiency of the frame only is 29 /
0,55 = 52 %.
We have
considered the glide and the level flight. Let's go a little bit
further and study the climbing with a climb angle A.
On a level
flight (cruise), you can consider the thrust force Fp we have seen
above is used to compensate for the drag. During climbing, the
required force F will have to compensate for not only the drag but
also an additional force which is in fact the projection of the
plane's weight on the flight line, that is to say m * g * sin (A).
And therefore:
F = Fp + ( m
* g * sin (A) ) or F = ( m * g / f ) + ( m * g * sin (A) ) and then:
sin (A) = (
F / P ) - ( 1 / f )
Still in the
case of the "Magicien d'Oz", the maximum thrust ( at full throttle )
given by the propeller is 15 gramme-force and the maximum climb angle
is defined by sin (A) = ( 15 / 31 ) - ( 1 / 7,22 ) = 0,345 and
therefore : A = 20 degrees.
|
|
Back to home page:
|
