June 2007 51
BY A.G. “ANDY” LENNON
Matchmaking
Match a model’s performance
to a pilot’s skill level
MATCHMAKING PROPOSES a logical
engineering approach to selecting a model,
engine, and propeller, and the
combination’s performance and flying
characteristics will be a match for the
pilot’s flying-skill level—or for a beginner
with no flying skills at all.
This article includes simple formulas
involving public-school arithmetic that are
easy to solve on an inexpensive pocket
calculator. It needs to be the “scientific”
type, which has square (x2) and square
root (√) buttons.
The article is divided into sections that
cover the model, the engine, estimating
thrust, selecting a propeller, and
information sources. It is aimed toward the
beginner but contains information that will
be of interest to the expert.
The Model: A beginner needs a stable,
relatively slow-flying airplane that
virtually flies itself and has limited
aerobatic capabilities. Its basic
specifications include a .40-size engine, a
700- to 800-square-inch wing area, and a
wing loading that does not exceed 20
ounces per square foot of wing area.
This aircraft’s airframe will have high
drag from an exposed engine and large
wheels on its tricycle landing gear, which
will allow for a steeper glide slope that
makes judging landing approaches easier.
It will have full proportional control of the
ailerons, elevators, rudder, and throttle.
The student is well advised to join a
local RC flying club. Most have
experienced pilots who instruct. They will
check the model for the correct CG
location, fully charged batteries, a fueled
tank, and correctly functioning controls.
The instructors will start the engine and
adjust the needle valve for high rpm and
idle, and then test-fly and trim the airplane
for level flight. They will stand by the
novice as he or she flies the model, and
they will be ready to take control if
problems arise until the beginner has
developed adequate skills to fly alone.
The expert flier wants high power in
relation to his or her model’s weight, to
pull the airplane easily and smoothly
through maneuvers that include sustained
vertical climbs. The aircraft must have
relaxed stability for good aerobatics, and
high wing loadings with fast takeoffs and
landings are no problem for this pilot.
Popular models for the expert are scale
versions of aerobatic monoplanes and
biplanes, such as the Extra 300 and the
Ultimate biplane. RC Aerobatics pilots
fall into this category.
The rest of us fliers fall somewhere in
between the beginner and expert
classifications. Table 1 provides
suggested parameters for all three classes
of pilots.
Power loading (PL) is a convenient
way to relate weight to power for
comparison purposes. A model that
weighs 92 ounces and is powered by a .46
two-stroke engine would have a PL of:
92 ÷ .46 = 200 ounces/CID
A 175-ounce model powered by a l.20
CID engine has a PL of:
175 ÷ 1.20 = 145 ounces/CID
To select an engine’s displacement
requires the model’s weight and the PL to
be selected. The formula is:
Model Weight (ounces) ÷ PL (ounces/CID)
= Engine CID
For a model that weighs 100 ounces
and has a PL of 250 ounces/CID:
100 ÷ 250 = .40 CID engine
In my experience a two-stroke PL of
200 ounces/CID permits a sustained
vertical climb to almost out-of-sight
altitude.
The Engine: The power of an engine is
expressed in two ways: torque and/or
brake horsepower—both at specific rpm.
Torque is the elemental force that
rotates the propeller. To obtain the
maximum thrust, the propeller’s diameter
and pitch should load the engine to an
rpm of the highest torque.
Figure 2a illustrates the output of a
.61 CID engine, which is an excellent
sport power plant. The torque curve is
almost level, peaking at 10,500 rpm. This
engine can effectively rotate a wide range
of propeller diameters and pitches: large
diameter and low pitch for slow-speed
flight or smaller diameter and larger pitch
for faster speed.
Sport engines operate in a 6,000-
13,000 rpm range. The large engines
develop their maximum torque at the
lower rpm.
Brake horsepower is a calculated
figure. It is:
Torque (inch-ounce) x rpm ÷ a constant
number (engine expert Dave Gierke uses
1,008,000).
Increases in either (or both) torque
and rpm will result in an increase in
horsepower. The rpm figure is increased
by using small propellers with low pitch,
which reduce the load on the engine.
These propellers are too small for
practical sport-model flying.
Some engine manufacturers have
adapted racing-engine technology to their
power-plant designs. That moves the
peak of the torque curve closer to peak
rpm, further inflating the horsepower
output, but to the detriment of torque in
the sport rpm range. See Figure 3.
The automotive people are more
candid. They advertise horsepower and
torque, such as “200 horsepower at 6,000
rpm = 275 foot-pounds of torque at 4,400
rpm.” Ads in model aviation magazines
quoting “1.6 horsepower at 16,000 rpm”
have little significance for practical
propeller selection. Torque is the figure
to use.
Model engines fall into the three
following groups.
06sig2.QXD 4/23/07 12:45 PM Page 51
Speed Wing Loading
Class (mph) ounces/square foot Two-Stroke Four-Stroke
PL
(ounces/CID)
Expert 100-125 25-35 100-200 90-180
Intermediate 80-100 20-25 200-250 180-225
Beginner 60-80 15-20 250-300 225-270
Table 1
Figure 2a
Pusher propeller designs are typically high-speed aircraft.
The correct propeller will allow the engine to unload enough
thrust to carry the heavy wing loading.
Scale aircraft have engine needs that often go beyond propeller selection. Engine
sound adds realism, and selecting the right combination can improve judging scores.
1) The engine has had a review published
that provides the horsepower and torque
curves along with a tabulation of rpm for a
range of suitable propeller diameters and
pitches for that engine. Figure 2 (a and b) is
typical.
2) The engine has been reviewed, but only
the tabulation of propeller rpm is quoted.
3) The engine has not been reviewed.
Thrust Estimating: A propeller rotating at
high rpm blasts a column of air backward.
The equal and opposite reaction (Newton’s
third law of motion) propels the airplane
forward.
The air coming off the propeller has
volume weight and velocity. Air weighs
1.22416 ounces/cubic foot at sea level. It is
possible to calculate the weight of this air
blast, providing thrust/second. I have
developed a simplified formula for thrust
estimating. It is:
Diameter2 (inches) x nominal pitch x static
rpm x .000011127 = thrust in ounces/second
at sea level (See altitude definition for
modified constants for high altitudes where
air weight is lower.)
A 10-inch-diameter, 9-inch-pitch
propeller turning at 12,000 rpm would
have a thrust/second of:
102 x 9 x 12,000 x .000011127 = 120 ounces/
second
Knowing the model’s weight and the
thrust/second, it is possible to determine the
thrust-to-weight ratio (TWR), measured in
percentage. A 92-ounce model (my Swift)
with a thrust of 120 ounces/second has a
TWR of:
120 x 100 ÷ 92 = 130%
RPM
CORR.BHP
TORQUE (oz.-in.)
52 MODEL AVIATION
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June 2007 53
An Aerobatics model requires the right balance of thrust for
strong vertical performance, but also needs to be quiet to
adhere to AMA noise rules.
Figure 3
APC Propeller rpm Thrust Speed
Diameter x Pitch ounces/second (mph)
11 x 7 13,400 126 110
12 x 6 13,400 115 82
12 x 8 10,500 134 95
12 x 6 10,100 133 80
Figure 2b
Figure l estimates the model’s speed using the propeller’s nominal
pitch and rpm. The TWRs are calculated for 14 models’ performances I
have observed many times.
It was concluded empirically that the TWR is proportional to the
angle of climb the model can sustain indefinitely. See Table 2.
TWR percentages are a more accurate appraisal than PL because
engines with the same CID but different manufacturers are not equally
powerful.
If you have an engine and are seeking a model for it to power, the
TWR may be used. Assuming a thrust of 134 ounces/second:
TWR Model Weight (Ounces)
125% 107
100% 134
75% 178
50% 268
The formula is:
Thrust/Second ÷ TWR = Model Weight
That torque should be used for propeller selection. Consider the
MDS .46 engine. Table 3 tells the story.
Propeller Selection: The objective is to select a propeller with a
diameter and pitch that loads the engine to or close to its peak torque
and propels the model, in level flight, at the preselected speed. The
procedure is different in each of the three engine groups I listed
previously.
Group 1) Brake horsepower, torque curves, and rpm table
available.
Refer to Figure 2 a and b. Propeller selection is easy. The maximum
torque is 10,500 rpm. The rpm table shows that a 12 x 8 APC propeller
turns at 10,500 rpm.
However, at 8-inch pitch and 10,500 rpm, Figure 1 indicates a
speed of 95 mph. This is too fast for our pilot; he or she wants 70 mph.
Referring to Figure 1 again, a 6-inch pitch at 10,500 rpm gives 70 mph.
To determine the propeller diameter with a 6-inch pitch that will
provide the same load as the 12 x 8, see Figure 4. It is based on Dave
Gierke’s Propeller Load Factor (PLF) of Diameter2 x Pitch = PLF.
Applying this to the 12 x 8 propeller produces a PLF of 1,152. For the
14 x 6 the PLF is 1,176, which is close enough for all practical
purposes.
If the expert pilot requires a higher speed than 95 mph, he or she
will follow the same procedure, but select a higher pitch, at the same
rpm (10,500) that will give the required speed and use the formula to
obtain diameter.
RPM
CORR.BHP
TORQUE (oz.-in.)
06sig2.QXD 4/23/07 1:12 PM Page 53
Warbird models are
famous for high-speed
low passes. The
airplane’s smooth
outline means it
requires a lowerpitch
propeller.
A 60-size model will often fly as well with
two .25 engines (less displacement).
Static rpm
x 1,000
Level Flight Speed
(mph)
Normal Pitch
(inches)
Figure 1
Figure 4
4 18.3 4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
20
25
30
35
40
50
60
70
80
90
100
150
200
250
300
350
400
450
500
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Group 2) Only rpm table available.
Refer to Figure 2b: the table of rpm for a .61
engine, calculated thrust, and speed. The 12 x 8
gives the most thrust, but notice how close the
others are in thrust and note the speeds. For our
pilot who wants 70 mph, proceed as in Group 1
to obtain pitch + diameter with a PLF that is
close to that of the 12 x 8 propeller.
Group 3: No published review.
Unless you have a friend, with the same
engine, who can be persuaded to develop an
rpm table (Figure 2b) for suitable propellers,
the only thing to do is obtain the engine and
bench-test it to develop an rpm table
specifically for that engine—after carefully
breaking in the new engine.
Then proceed as for Group 2, calculate
thrust/second, and estimate speed from Figure
1. Select the propeller that produces the highest
thrust. It will be close to the engine’s peak
torque. Modify the diameter and pitch to obtain
the selected level flight speed, as detailed in
Group 1.
Information Sources: To assist the beginner in
the selection process, following are sources of
information.
• Engine, kit, or ARF reviews in model aviation
magazines.
• Catalogs from distributors such as Tower
Hobbies. They contain a wealth of information
about models, engines, propellers, and
hundreds of accessories.
• Dave Gierke’s thorough and comprehensive
engine evaluations published in Model Airplane
News: “.40 Engine Shoot Out” in the March
2001 issue and “We Test 10 .60 Engines” in the
May 2003 issue.
Thanks to friend and fellow author Dave
Gierke; his work made a major contribution to
this article.
Happy Landings! MA
A.G. Lennon
487 Oakville Rd.
Dollard-des-Ormeaux
Quebec, Canada
H9G-1M1
√ Old Diameter2 x Old Pitch ÷ New Pitch = New Propeller Diameter
––––––––––––––––––––––––––––––––
√ 122 x 8 ÷ 6 = 13.85 inches in diameter (say 14 inches)
––––––––––
In the above example:
54 MODEL AVIATION
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June 2007 55
Model TWR
Propeller Thrust Speed (100-ounce
(Diameter x Pitch) rpm (ounce/second) (mph) model)
Max Torque 10 x 9 10,710 107 110 107%
Max Horsepower 9 x 4 18,000 65 80 65%
Class TWR Performances
Expert 110% and up Sustained vertical climb, high maneuverability
Intermediate 85 to 110% Sustained steep climb, good maneuverability
Trainer 65 to 85% Modest climb, low maneuverability
Glow-Powered Glider 25 to 65% Shallow climb, poor maneuverability
Table 2
Multicylinder engines have special
propeller requirements ranged to suit
their limited performance.
Table 3. This presents solid proof that choosing a propeller diameter and pitch that loads the engine to peak torque rpm is
superior to loading it to peak horsepower rpm.
A two-stroke .46 engine can use any of more than a dozen 9- to 11-inch-diameter
propellers. One of those will be right for the aircraft and the pilot combination.
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