Model Propeller Constants - Weick, Durand and Lesley

"Aircraft Propeller Design", written by Fred E. Weick and published by McGraw Hill Book Company in 1930 makes reference to wind tunnel test results for a series of propellers with pitch to diameter ratios between 0.5 and 1.1, see pages 105 to 108 . The tests of these 13 propellers performed by W. F. Durrand and Everett Lesley are reported in "TESTS OF THIRTEEN NAVY TYPE MODEL PROPELLERS", NACA TR 237, 1926 .   You can find out more about the tests at Durand Lesley Propeller Collection and download the test report at NACA TR 237 .

In 1994 I, Chris Stoddart, developed and posted to the internet a mathematical model based on these tests and Fred Weick's Representative Section / Blade Element theory, weick.tk.  The model made use of MiniTK a free version of the TK Solver, a mathematical modeling and problem solving software system based on a declarative, rule-based language, commercialized by Universal Technical Systems, Inc. , see TK_Solver at Wikipedia  and UTS .  The free version can still be used as a DOS application in Windows and with Linux.  You can download MiniTK from  MINITK and the Weick.tk mathematical model from Weick.TK .

Weick.TK allows the examination of many interactions on propeller performance on parameters such as efficiency, power and thrust as effected by pitch, diameter, velocity, and rotational speed and other factors.  The program can select an optimal propeller to match a flight condition. It gives reasonable answers to queries ranging from rubber power to control line speed.

The Rule, Variable, and Unit sheets of Weick TK appear below.

Rule Sheet

Status	Rule
Comment	;Program - Weick.tk, Written by Chris Stoddart, July 23, 1994
Satisfied	eta=TAN(PHI)/TAN(PHI+GAMMA)
Satisfied	C_p=QGF*B*WR*J^2*((TAN(PHI)+TAN(GAMMA))/(TAN(PHI)*SIN(PHI)))*C_L
Satisfied	C_s=J/C_p^0.2
Satisfied	C_s = V*(rho/(P*(N/(2*pi()))^2))^.2
Satisfied	eta=C_t*J/C_p
Satisfied	BETA=ATAN((4*PoverD)/(3*PI()))
Satisfied	TAN(PHI)=V/((3*D/8)*N) ;-- use without inflow
Satisfied	ALPHA=BETA-PHI
Satisfied	C_L=0.355+4.3*ALPHA-3*(ALPHA+0.075)^2 ;-- use without inflow
Satisfied	GAMMA=0.47*ALPHA+0.0073/(ALPHA+0.075) ;-- use without inflow
Satisfied	GAMMA=ATAN(1/LovrD)
Satisfied	T=(rho*C_t*N^2*D^4)/(2*pi())^2
Satisfied	P=(rho*C_p*N^3*D^5)/(2*pi())^3
Satisfied	Q=P/N
Satisfied	M_0=T/P
Satisfied	J=V/(D*N/(2*pi()))
Satisfied	PoverD = Pitch/D
Satisfied	WR = Chord/D
* Undetermined condition	IF OPT = 'yes THEN ALPHA = .8/57.3

Variable Sheet

Status	Input	Name	Output	Unit	Comment
					File Name: weick.tk July 23, 1994
	.579	D		m	Diameter
	.722	Pitch		m	Geometric pitch
		Chord	.06948	m	Chord at 3/4 distance to tip
	2	B			Number of Blades
	.12	WR			Width ratio at 3/4 distance to tip
		PoverD	1.24697754749568		Aerodynamic Pitch over Diameter
	8	N		rev/s	Angular velocity
	5	V		m/s	Forward velocity
		T	1.06051082397811	N	Thrust
		P		w	Absorbed Power
		Q	.129313391262165	N*m	Absorbed Torque
		M_0	.163155511381247		Figure of Merit [T/P in N/w]
		J	1.07944732297064		Advance ratio V/(N*D)
		eta	81.5777556906235	%	Efficiency
		C_t	.120262549489696		Thrust Coefficient
		C_p	.159132947457634		Torque Coefficient
		C_s	1.55901190738972		Speed/Power Coefficient
		BETA	.486760145073151	rad	Geometric Angle of Attack
		PHI	.429595614242357	rad	Relative Wind Angle
		ALPHA	.0571645308307935	rad	Aerodynamic Angle of Attack
		C_L	.548405092943241		"Lift Coefficient" Correlation
		LovrD	12.1526639689179		"Lift/Drag ratio" Correlation
		GAMMA	.0821015133831694	rad	Angle who's tangent is Drag over Lift
	1.226	rho		kg/m^3	Air density
	.366372781256872	QGF			Overall torque grading factor (0.366)
		OPT			To find optimal Pitch given D,HP,N,V
					enter 'yes, otherwise leave blank

Units Sheet

From	To	Multiply By	Add Offset	Comment
m	in	39.37
ft	in	12
m	mm	1000
kg	g	1000
rad/s	RPM	9.549296585513721
m/s	ft/s	3.280833333333333
w	hp	.001342281879194631
rad	deg	57.29577951308232
N*m	lbf*in	8.850748065226473
lbf*in	ozf*in	16
lbf	ozf	16
w	J/s
N	lbf	.2248090247334889
N/w	lbf/w	.224809024733
lbf/w	ozf/w	16
rev/s	rad/s	6.283185307179586
ft/s	MPH	.6818181818181818
w	HP	.001342281879194631
lbf*in	gf*cm	1153.16
-	%	100
lbf	gmf	454
ozf*in	gmf*cm	72.07250000000001

SCRAM Plans

In issue 37 Sergio Montes and Andrew Longhurst present an article to celebrate "The 60th ANNIVERSARY OF SCRAM, Laurie Barr’s LIGHTWEIGHT CONTEST MODEL".

SCRAM Plan

The printed edition of issue 37 contains a full size plan on 4 pages.  As a service to our subscribers that prefer not to unstaple their printed edition or those that receive the Digital Edition the links below provide access to a a full size plan and files for printing on typical personal printers on either A4 or Letter size paper.

Full size plan

Tiled plan for A4 size paper

Tiled plan for Letter size paper  

EIFELPOKAL 2010 - Allard van Wallene

An active low over northern Europe colliding with warm air in the south caused massive rainfall over Holland and parts of Germany. Showers were of a clustered nature with sometimes thunder and lightning under massive towering cumulonimbus clouds. To avoid the heavy Friday afternoon traffic, I left early. In the car I played an audio book on the stereo, but my mind was with model flying, so I changed to the local radio station. They were playing a series of ‘rain’ songs: ‘Its Raining Men, Its Raining Again’ and more. Come to think of it, there are plenty of rain songs! At the German border, the station got too weak for proper reception, but the weather continued the sentiment, with massive downpour.  Visibility dropped to dangerous levels and luckily some cars used their fog lights for me to keep track. Upon arrival at the field, the F1B and C contest was well on its way. There were grey skies all around and a slight drizzle.

Line up of shelters on F1B day

 

A heavy shower had just moved out and it had struck lighting right in the middle of the field. The cars were shaking on their wheels! The organizers were very flexible all through the event by halting a round whenever deemed necessary. Nevertheless, some flyers were caught downwind by the rain. Later that day, the wind shifted from NW to N, straight over a downhill slope. Only a good climb and good air could secure a safe passage and a max which was set at 150 seconds. The fly off was scheduled for 6.30 the next morning. Bernd Silz once again managed the best time and Seydel topped F1C.

Aringer with flapper

That night we enjoyed dinner at an Argentinean restaurant, which I visited some years ago with Anselmo Zeri. A good choice of quality beef and discussions about F1A technology made us forget the weather outside.

Next morning dawned with moderate wind and partly overcast skies, which lasted for two rounds. Like the previous years, right at the start of round one, small patches of lift were available. The big question was if they would carry the model high enough to clear the dropping slope at the south end of the field. The wind was still well within comfortable limits and I decided to take my Ex Span for a safe max. The model climbed away gently and although the slope pulled the model lower, it maxed at some 70 meters altitude. Also in round two, the wind kept a low profile, and some sunny spells made us even forget the wet of the day before. After a few minutes a large thermal passed through. I prepared for launch while others were already launching their ships. After my launch I looked up and saw something dangling from my stabilizer. Darned, towline over the stab I thought. But the towline was on the ground still in one piece. I looked up again and saw the entire top cover had stripped off the stabilizer! The model tried to stay in the thermal, but the drag proved to be too much and it slowly descended. I watched the flight in awe, before winding up my towline. I slowly strolled downwind to collect the model. Tough break, I thought. In round three Siggi Limberger walked up to me. “What a great flight that was”, he said. I was puzzled. I explained what had happened to my model, and he replied he and the timekeeper had seen my towline over the stab, which then dropped away for the model to max at great altitude. I had no clue what had happened or which model they followed, but 180 was on the scoreboard! Undeserved for sure, but I never argue with timekeepers!

Seydel programs his winning model using Sidus electronics.

The weather forecast was all over the place but the promised improvement of the previous day was over optimistic. Soon massive towering cumulonimbus clouds were approaching from the horizon in round three, the kind jetliners would take a detour for. One of such clouds managed to hit us during lunch break and part of the 4^th round. The organizers managed quite well in halting the round and continuing after the rain had passed, in particular with the previous day’s lightning strike still fresh in memory. Although the average wind speed was around 6 m/s and less than last year’s, the turbulence levels were particularly high. Picking your own air proved to be the best way for a secure max as thermals were often small and passed at high speed. The harsh conditions made towing a real challenge. Putting up a fight for 20 minutes and maxing at great altitude made the experience the more rewarding. In round 5 the thin spectra towline was wrapped around one of my left hand fingers. The fierce turbulence required full control over the towline all the time, so my finger obviously didn’t cooperate! My model towed-in and after the adrenalin faded away, the cut in my finger made me realize I should use a left hand glove as well. After the 7 rounds only 3 managed a clean score, Uwe Rusch, Ivo Kreetz and yours truly. The fly off was delayed to make sure the threatening clouds stayed clear from the field. After another shower passed through, weather conditions were perfect: about 4 m/s wind and sunny. But with wind from the north, such conditions can be very tricky. While towing, all three of us felt a nice thermal. I launched first, but the towline slipped from my hand and the model pulled out of the bunt not in the position I wanted it to. Then Ivo launched, the model pitching up too much. The bunt redirected the model back to a near horizontal position and a stall followed. None of our models climbed away and again the Zulpich air had fooled us. Uwe Rusch launched shortly after, and although he managed to beat our times, also his flight was not supported by any clear thermal activity. I ended third only 2 seconds behind Ivo. Our models could be retrieved from a close distance with all flights being between 3 and 4 minutes.

It seems like a chain of warm weather has been replaced by the type of weather we were used to in the eighties and nineties. Thanks to today’s carbon composite structures, many coped pretty well with the weather. We all feared we would need our rain gear for the years to come, the seven fat years now being followed by seven lean years.  Future will tell if this holds true.

First two rounds were blessed with decent weather

Starting line close to camp site, and wind of course.....

F1A winners

Website Rewritten

The Free Flight Quarterly website has been completely rewritten using WordPress.  This was done to make the website both easier to use and to maintain.  It is anticipated that further changes will be made in the future.

The website can be reached at http://freeflightquarterly.com/wordpress/ or at the old address of http://www.freeflightquarterly.com where you will be automatically redirected to the new web site.  

Swedish and Nordic Cup 2010 - Allard van Wallene

Just when a major heat wave was sweeping the western parts of Europe, the weekend for the Swedish World Cup was rapidly approaching. Temperature forecast for the Friday in Holland was 36 degrees, in Sweden some 10 degrees less. Ivo and I decided to leave early. And leaving from Ivo’s place at 6 AM meant I had to leave at 5. Good thing I'm an early riser! Weather was excellent all the way up to Rinkaby, the venue of both competitions. But first we headed off straight to the Ahus pizzeria to watch Holland play the quarter finals soccer world champs against Brazil. We arrived just in time, some 10 minutes late after Brazil scored the first goal. The restaurant was packed with dutch flyers, I guess the locals never knew why a group of Dutch fans would drive all the way up to their pizzeria to watch the game! Soon the spirits rose after Holland started scoring. Great fun, and the quality of the pizzas added to the spirits. The fatigue of traveling vanished into thin air, and we would have plenty of that stuff the coming days!

We recharged our energy levels enough to check in our stuff in the barracks and do some flying. Upon arrival at the west side of the field, the fly off of the Swedish nationals was on its way. We tested some of our models. Thomas Weimer, who flew the small classes earlier that day, warned us for the tricky thermals. It later proved to be the understatement of the year.

Antoon (r) congratulating Jari with Swedish Cup victory (Schwendemann photo)

The next day dawned with blue skies and some 3 m/s wind, identical conditions as the day before. Thermals were present but could collapse in no time. To be honest, we never experienced anything like it. Even ace flyers like Findahl, Hellgren, Persson and Holbom had difficulties finding good air and keeping the model in thermals. Sub maxes started to appear on the scoreboard at a rapid pace.

Must by fly off time!

Remarkable to see that some designs could handle the tricky thermals pretty well by keeping a tight turn, while other models just wondered about out of the good air. If there were any conditions to check wing warping and centering ability, this was the ultimate trial. Despite the tricky conditions, some managed to max out using utter concentration. Since the fly off was scheduled at 7.30pm, there was some time for lunch and rest. The first fly off round saw some good thermal activity, but only Antoon van Eldik and Jari Valo managed a solid max. F1B saw similar conditions with only Rosonoks en Stendal maxing. In F1C nobody had maxed out and Juri Roots showed the best climbs all day to secure a first spot, but with Pieter de Boer only 7 seconds behind. F1Q showed the first results of the rather liberal model specifications. Matti Lihtamo had worked hard over the past year to come up with a box full of extremely hot models. With a 1 kw motor it outclimbed even the best F1C model. When launched it accelerated so fast it was hard to catch it by camera. Ten seconds motor run would have been more than sufficient as the last 5 seconds of the 15 second motor run, the model got out of its climb pattern and needed about half the attained height to recover due to its low stability margin, still more than enough to beat Andreas Lindner. The second fly off in F1A saw different conditions. Thermal activity had died out almost completely. Jari decided to make a dash to the north east corner of the field where he could benefit from unobstructed upwind area and therefore turbulence free air. He towed patiently for good air. A great launch followed with a rock steady glide to beat Antoon with more than 2 minutes difference. F1B had a similar show down. Remarkable to see the flyers could bring and use their own timekeepers, which led to some commotion among the two contenders with a model being ‘followed’ which had already landed. The many binoculars pointing in the right direction sorted that out quickly and Hagen Stendal topped Rosonoks by (at least) 10 seconds. A rotation of timekeepers could have easily avoided this unrest.

Antoon in utmost concentration programming his ship.

After this thrilling fly off, we retired to the barracks to eat some of our noodle fast dinners, which tasted remarkably well. Right after we finished the prize giving was on its way with the traditional cookies, soft drinks and (cool!) beers. The prizes were beautifully crafted blue glass sailing boats. That night, Germany was playing against Argentina and by the cheering noises through the barracks one could keep track of the scores.


The next day the movement of the trees announced a bit more wind compared to the day before, but the clear blue skies and wind direction were signs of another tricky day for this year’s Nordic Cup. And tricky it was: Kosonoshkin, Assmuss and Valo managed to make only one single max, Anders Persson (2008 winner) no max at all. Your’s truly was thrown out of good air in the very first round after having launched high in what appeared to be good lift. Antoon van Eldik was like the days before, going strong for another clean score, but bad air spoiled his chances in the very last flight: 52 seconds.

Nordic Cup winner Ivo Kreetz (L) and Mike Holmbom

The downdrafts were particularly vicious. The one-liner of this weekend came from Michail Kosonoshkin: “Hey Antoon, I make only one max today, but I still beat you!” This summarized the tricky conditions. Ivo Kreetz, who damaged his Baldrick on a row of rocks the day before, had to switch to his old but reliable ‘service canon’, a short stubby model with low cambered thick airfoil. This model could handle the conditions particularly well, by sticking to the thermal like no other model. All flights were very high and one could see his confidence growing by the round. After the last round, only two maxed out, Ivo and Petri Kuikka. The F1B models could apparently handle the condition lots better with 9 (!!) flyers maxing out, almost half of the competitors attending. Also in F1C 3 out of 4 maxed out and it was again Roots beating Pieter. In F1Q it was once again Matti Lihtamo, but this time his opponent was Ron Assmuss who did somewhat better compared to his F1A flights. The rest, food, rest and fly off schedule was identical to the day before, although the wind was some 1 m/s stronger. Shortly before the fly off we learned that Anselmo Zeri had passed away. This gave Ivo and me a big dent in our spirits, but decided that Anselmo wouldn’t have it any other way than winning this event. The F1A fly off was soon on its way. The starting position was close to the south east tree line which marked the very edge of the field. Kuika moved away from Ivo and was battling the turbulence, circling his model dangerously close to the ground at times. Thermals were absent, and Ivo made a good launch to some 75 meters, a couple of meters more than Petri. This extra altitude made the 16 seconds difference for Ivo to win. Ivo’s flight of 220 seconds traveled almost the full length of the field. Quick math yielded a 6 m/s wind speed.


At the prize giving we had one minute of silence in memory of Anselmo Zeri who was a frequent visitor at the Swedish and Nordic cup. The prizes of this event were not the common trophies, but traditionally crafted ceramic dishes made by the wife of Tom Oxager.


This year’s events were blessed with fine weather but the trickiest thermal conditions ever seen. Many were getting desperate and started doubting either their flying skills, model quality or both. Judging the flight times on the result lists it was better to keep the trim of the models untouched, erase the downdrafts from memory and reboot the flying skills for the next competition. The memories of Anselmo however, will for ever stay with us…..

Beautifully colored glider

  

Jari with Tchop flapper, he didn't use it in competition.

Lihtamo's hottest F1Q in existence with 1kw motor. Catching this rocket on picture was more luck than anything.

[Original Posting by Allard van Wallene, July 11, 2010 - re-entered by Chris Stoddart July 12, 2010]