Main Menu Contact Us Order Now Free Flight Main Page

A Novel Method to Increase Participation
and Competition at Indoor Free Flight Contests

(With a Model Plan and Formulas for Predicting Flight Times)

From 31st Annual Symposium 1998
National Free Flight Society

ABSTRACT

    A method is described, which uses a mathematical model along with a programmable calculator to predict the maximum flight time of a rubber-powered indoor free flight model aircraft and to then establish a handicap. This handicap will create a more even playing field for contestants, with varying skill levels, who compete in a single event. It is also very useful for

combining events and skill levels when participation is limited. Click here for a plan, for an A-6 class indoor free flight model, is shown. Instructions are shown on the plan for an easy-to-make, portable weigh-scale designed to obtain the information needed to use the handicapping system. (Note that the gram scale is in inches and can be used as reference when copying/ photocopying the plan to full size.)

INTRODUCTION
    How many times have we heard the comment "I'm not going to enter the contest because I don't sand a chance against the experts" or, we go to a contest with low turnout of modelers and only one or two models are entered in each event? It would be beneficial if there was a way to make most of the models and contestants more competitive. Such a method has been developed and successfully used for several years at local contests.
METHOD

    The methodology is based on a number of mathematical equations which predict the flight performance of free flying model aircraft. The result is an estimate of the maximum flight time that might be expected from a specific aircraft under the influence of a number of variables. This maximum time, when compared to the mean maximum flight time for the class, results in a handicap number. The mean maximum flight time than becomes the reference against which all subsequent flights are compared. Each contestant's future flight time scores are multiplied by the handicap value derived for that specific model. The result is then entered as the adjusted score.
    It must be noted that only variables like the weight of the rubber motor and the airframe weight along with the

propeller design, are compensated for by the handicapping system. While this makes for a more competitive environment for the beginner, it does not take into consideration the skill and experience of the seasoned competitor when it comes to the subtle nature of trim and power matching that is so necessary in order to obtain maximum performance. An unlimited ceiling height is assumed and models in monoplane events, like Mini-stick, A-6, Easy-B, Penny Plane, and similar stick model events quality.
    In order to make the calculating process more rapid and user-friendly, a software program suitable for a programmable calculator like the Texas Instruments TI–85 is shown.
MATHEMATICAL MODEL

     Model Performance Analysis by Enkenhus defines the expected flight time to be equal to, the energy supplied by the rubber, multiplied by the propeller efficiency, divided by the product of the drag and flight speed.

T is in seconds, ER is the energy of the rubber in ft.lbs. per lb. of rubber, WR is the weight of rubber in lbs., P is the propeller efficiency value, D is the drag in lbs., and V is the flight speed in feet per second.
     A measure of the energy (ER) stored by a twisted rubber band, and which is available to turn the propeller, is rather difficult to accurately determine. Tests performed on Tan II indicate an average ER of 2700 ft.lbs. Per lb. Data provided by the rubber supplier are often in the order of 4000 ft.lbs. Per lb., but these are most likely values obtained from stretch tests and do not account for frictional losses in the system.
     WR is the weight of the rubber motor, usually weighed in grams and then converted to lbs. The Gram Scale shown on the A-6 model plan is a convenient instrument for weighing rubber motors.
     Propeller efficiency (P) may be estimated as:

 

     CL is the coefficient of lift, AW is the wing area in sq.ft., RL/D is the lift-to-drag ratio, and AP is the area of the prop in sq.ft. The fractional number L is approximately 0.85 for efficient helical pitched props. Experiments indicate that L can be as low as 0.5 for the inefficient flat paddle blade propellers found on many models designed for beginners — models like the A-6.
     Drag (D) is equal to the weigh of the rubber (WR) plus the aircraft weight (WA), divided by the lift-to-drag ratio (RL/D). D is in lbs. WR and WA are usually measured in grams and then converted to lbs.

The flight speed (V) may be calculated as:

V is in feet per second, WR and WA are in lbs. And the wing area (AW) is in sq. ft.
     Indoor Glide Tests by McCombs describes a very good way of obtaining the lift-to-drag ratio (RL/D) and the coefficient of lift (CL). For the indoor stick models mentioned earlier, experiments show that an average value of 4.0 is a good compromise for RL/D and 0.9 is a suitable average value for CL.

PROGRAM FOR THE TI-85 CALCULATOR

PROGRAM:HANDICAP
:Lbl 1
:ClrHome
:Menu("SELECT MODE","ONE DESIGN",3,"MIX DESIGN",4,"SET PARAM.",2)
:Lbl 2
:Input "L/D=,C
:Input "ER=",E
:Input "CL=".I
:Input "MFT FOR CLASS=",J
:Lbl 4
:Input "CHORD=",F
:Input "SPAN=",G
:Input "PROP DIA.=",H
:Menu("PROP TYPE","HELICAL",5,"PADDLE",6)
:Lbl 5
:0.85 > L
:Goto 3
:Lbl 6
:0.65 > L
:Lbl 3
:Input "WR=",A
:Input "WA=",B
:((A+B)/(28.35x16))/C > D
:sqrt (((2(A+B)/28.35x16))/((.0023xIxFxG)/144))) > V
:L/(1+((IxFxG/144)/(2xCxpi(H/2)2/144))) > P
:(E(A/(28.35x16))P)/(DxV) > T
:Fix 2
:Disp "MAX TIME(SEC)=",T
:Pause
:J/T > K
:Disp "HANDICAP=",K
:Pause
:GOTO 1

USING THE PROGRAM
1. After starting the program, SELECT MODE 3 (SET PARAM.).
2. Enter L/D=4, ER=2700, CL=0.9 and MFT FOR CLASS=360 (this is the mean flight-time in seconds for an average model. Five minutes is shown, although this is not an important number as long as it is not changed during the contest).
3. Enter the wing CHORD= and the wing SPAN= of the model in inches.
4. Enter the prop diameter PROPD= in inches and select the prop type.
5. Use the GRAM SCALE or other suitable weighting device, weigh the rubber motor in grams and enter this value into WR=, then do the same for the aircraft without the motor, entering this value into WA=.
6. The calculator will display the maximum flight-time that can be expected from the model
7. Press Enter and the calculator will display a number after HANDICAP=. This number should be recorded for that specific model and later used to calculate the adjusted flight-time score. Multiply all subsequent flight times, in seconds, for that model by this handicap value. Each model will have its own specific handicap.
8. Pressing Enter will now take us back to the SELECT MODE menu. If a ONE DESIGN event is being held, select 1 and WR= will be displayed. If events are being combined or a single event has a variety of designs, then select 2 and CHORD= will be displayed. Now enter data for the next model.
RESEARCH MODEL AIRCRAFT
     The RAFTER ROCKET Easy A-6 model was the prototype for the development of this work. It is an entry-level design suitable for beginners. To guarantee flight success, a few notes are in order. Before gluing the wing mounts to the motor stick, assemble the fuselage, prop, tail boom, stab and fin. Hook up a 12" loop of 1/16" rubber. Loop it into four strands so that it is tight between the hooks. Now find the balance point of this assembly and mark on the motor stick. Mount the wing so that the rear post is at this mark. The centre of gravity is now properly located.
    Set up the model using the rear-view sketch. Adjust the wing incidence until good flight characteristics are obtained. Some left thrust may be needed. Wind the motor as a single loop, varying the length to obtain the best climb. The handicapping system will always keep the model competitive as long as the model lands with a few turns left on the motor.
GRAM SCALE
    The paper clip weigh-scale shown on the model plan is very useful for measuring the weight of the rubber and airframe. ACCO #1 paper clips are recommended for the wire parts. Hook the clips together to form a chain of suitable length or weight. Without a counterweight on the scale, hook enough clips together for the scale-balance, snipping off short lengths of wire until the scale is horizontal. Use a top door jamb or wall/ceiling line as a reference. Make a one-gram counter-weight by hooking together 2 1/2 clips (clips weigh 0.4 gms   each) and slide it along the scale until an unknown weight on the hook results in the scale assuming a horizontal attitude. Read grams off the scale. If a greater range is needed, make up a heavier counterweight and multiply its weight by the scale number.
     An accurate calibration of the scale is not needed to effectively use the handicapping system as long as this scale is used to weigh all of the models.
SUMMARY
     The mathematical model employed to predict the flight durations in this work, exercises a few liberties in some of the assumptions and data precision. Even so, it has proven to be a useful tool, making many a contest more enjoyable. The author had the opportunity of testing the accuracy of the flight-time predictor when a Limited Penny Plane flight that didn't hit the ceiling of the Kibbie Dome in Moscow, Idaho, resulted in a flight time of 14 min. 3 sec. After arriving home, the airframe and rubber were weighed on an accurate scale and entered into the calculator. The calculator had been used at the   contest earlier in the year and nothing else was changed, as rubber from the same batch was used in all cases. The calculator result indicated that a maximum flight time of 14 min. 40 sec. was possible.
     The system seems to deviate in accuracy when applied to very small models. It predicts that a Mini-stick is capable of up to 20 min. flight durations. We will have to wait and see.
     More research on this system is ongoing to expand its usefulness into other events such as scale models and the like. Criticism and research assistance is enthusiastically welcomed.
REFERENCES
1. Enkenhus, K., 1978. Folkerts SK-3. Model Builder, Jan.: 48-49.
2. McCombs, W.F., 1996. Indoor Glide Tests for Evaluating Airfoils and Other Features. NFFS Symposium.

Published 1998 NFFS*

GizmoGeezer Products supports the NFFS and its efforts in keeping free flight modeling alive and well. Many great articles may be found in their publications. Order yours today from Robert McLinden at rmclinden@earthlink.net, 3903 West Temple Place, Denver CO 80236. Or visit the web site at www.freeflight.org.

*The National Free Flight Society (NFFS) is a nonprofit corporation, operating in conjunction with the Academy of Model Aeronautics (AMA), the National Aeronautic Association (NAA), and the Federation Aeronautique Internationale (FAI).

For other fantastic Geezer tales - click GG Stories and Plans