Investigating the lift force of a toy helicopter

Transcription

1 Investigating the lift frce f a ty helicpter I am an active member f my schl s aernautics club. We ccasinally fly gas pwered mdel aircraft and we spend endless hurs at the realistic cntrls f a cmputer based flight simulatr. I have always been fascinated by flight. Recently my physics teacher bught a neat little ty helicpter 1, ne that perates by batteries and infrared remte cntrl. This ty was the stimulus fr my required physics investigatin. A little helicpter thery research and the help f my teacher sn revealed an equatin 2 that gave me the purpse f my experiment, namely, t cnfirm the relatinship between thery and experiment. PE The student has sme interest here. This culd turn ut t be a gd IA. EX The research prject is defined and apprpriately extracted frm the relevant scientific equatin. Under Evaluatin, this is the research questin t be answered. As early as 400 BC the Chinese made ty helicpters. In 1483 Lenard de Vinci designed a wrking helicpter; we d nt knw if ne was ever made. Then in 1754 the Russian Mikhail Lmnsv develped a helicpter with a mtr. The first sustainable flight helicpter was make in 1860 in France, and the design has imprved every since. Frm 1922 t tday helicpters have played an imprtant rle in all aspects f aviatin. 3 S here is the helicpter equatin 4 : The rtatinal frequency f the rtr blade is dented f. Frequency is measured in hertz (Hz). The lifting frce F (measured in newtn s) is the frce required t make a helicpter hver in air with n up r dwn mtin. I think that the cnstant is derived by the thery f the equatin. The density f air, units f kilgrams per cubic meter,. Lambda,, is a parameter called the rtr inflw rati. Lambda relates t the flw f air abut the rtr. The radius f the rtr blade is R. Using Newtn s secnd law f mtin, I changed F int m g (mass and gravity) in the abve equatin. C Here and in a few ther places we find minr mistakes, but this des nt affect the verall investigatin. By varying the rtr blade frequency (by adjusting the mtr pwer supply) I then measured the lifting effect (n a digital balance). A graph f frequency squared again lifting mass wuld cnfirm r deny the equatin t my ty helicpter. The ther quantities, such Page 1 Physics teacher supprt material 1

2 as the value f gravity, the density f air, the rtr radius and the physical characteristic f the rtr inflw rati are all cnstants, s we can ignre them as far as testing the equatin. Unlike airplanes that have prpellers, helicpters have blades. Helicpters are als knwn as rtary wing aircraft. When helicpter blades are turning they hit the air and air is deflected dwnward, prducing lift. This gives sme lift and als reduces air pressure. It is cmplicated but explained nline. 5 With rtating blades the helicpter lifts ff the grund r, if frces (weight and lift) are balanced, the helicpter can hver at a fixed distance abve the grund. EX Mre technical details here wuld help the quality f the reprt. Lift is due t bth the pushing dwn f air by the blade and by a partial vacuum prduced abve the blade. If the student was curius they wuld have lked int this sme mre. When a helicpter is clse t the grund the helicpter experiences even mre lift, and this is called grund effect 6. This happens because the air is hitting the grund and bunces back. But the helicpter desn t require this in rder t fly. The air is cnstantly pushing back prviding the frce needed t create lift. Changing the angle f attack f the blades varies the amunt f lift prduced, in much the same way yu change the angle f attack f yur hand as yu hld it ut the car windw speeding dwn the freeway. Adjusting the entire plane f the rtr cntrls the directin f the lift. Tilting it frward causes the helicpter t mve frward 7. Here is the Ty Helicpter 8 I used the Extech Strbscpe Tachmeter strbscpe 9, mdel It has variable frequency and a digital readut. I cnsidered the uncertainty here t be ±1 Hz (ne digit f Page 2 Physics teacher supprt material 2

3 the least cunt). I adjusted the strbe frequency t btain a statinary and a single image f the rtr blade. I used an OHAUS digital balance 10 mdel Adventurer TM. It has a reslutin dwn t ne milligram, s the uncertainty was ±1 mg = ±0.001 g. The helicpter mass alne was g and the helicpter when at rest with the munting blck had a ttal mass f g. The quantity used in my investigatin is the unit f mass, which is nt the unit f frce, but the lifting frce is directly prprtinal t the calculated lift mass, hence my investigatin cncerns the lift mass f the helicpter as a functin f the rtr frequency. Althugh the digital balance reads mass t three decimal places, I did nt accept measurements with this precisin. The reasn was that when the helicpter engine was running there was sufficient vibratin and nticeable variable airflw and s that the digital balance reading kept changing. As a result, I culd nly read with cnfidence (that is, a steady value) t ne decimal place. Hence my lift mass uncertainty is limits t ±0.1 g. Analysis. I tk gravity as 9.8 N kg 1. EV The student is perceptive with cmments here and repeated elsewhere abut the quality f the data. A The student is perceptive here and makes a sund judgment abut an apprpriate uncertainty. I tk air density as 1.2 kg m 1. The rtr radius was measured t be 6.5 cm. Here is what I did. (1) First, I secured the helicpter t a blck f wd. My teacher suggested this methd. The wd mass was sufficiently large t keep the helicpter n the digital balance even when the helicpter is spinning its rtr at maximum speed. Then I read the balance value withut the mtr running. C There is a minr errr in the units f density but it des nt matter in this case. A Uncertainties here and with gravity and density are nt required. Significant figures are nt cnsidered, but again they are nt relevant. PE It is nt clear what the student designed and what the teacher r the jurnal article did. It turns ut that the student just cpied the methd, s there is little independent thinking r initiative here. PE It is clear that the teacher has infrmed much f this investigatin, thus restricting PE t levels f insight r creativity (neither f which are bvius thrugh the reprt). Page 3 Physics teacher supprt material 3

4 (2) I next started the helicpter engine by using the remte cntrl. I wre safety gggles and did nt stand t clse t the experiment. I als made sure ther students were nt near by fr safety sake. When the lwest pwer was applied, it was impssible t get a lw rtatin frequency. The mtr did nt mve until it started mving at the lwest frequency, f Lw, abut 74 Hz. The highest frequency, at the mst pwer, is dented as f High, abut 97 Hz. S that was my range f values. I wanted mre. EX The student tk apprpriate safety precautins. There are n ethical r envirnmental issues related here. (3) The mass lifted at any given frequency was determined by a simple calculatin. The lifting mass was: m Lift = m Statinary m Frequency. The lift prduced by the helicpter reduces the mass displayed by the electrnic balance. Increasing the amunt f pwer prduced increasing lift. The mass lifted by the helicpter is the difference between the mass at rest f the helicpter (plus wden platfrm) with n pwer applied and the mass reading when the rtr is spinning. I used a spreadsheet t d the calculatins. A This methd is simple, direct and mst apprpriate. (4) A graph f frequency squared against lift mass was then used t determine a linear and prprtinal relatinship and cnfirm the scientific thery. (5) The physical limits f the helicpter restrict the range f measurable frequencies and lift masses. I btained nly 9 sets f data, but this seems reasnable enugh. There were a few uncertainties in my experiment. A The helicpter characteristics clearly restrict the range f data, and nine values within this range is sufficient. Hwever, repeated measurement wuld be expected in this situatin. The least cunt n the mass measure was ±0.001 g. Hwever, my uncertainty here was much larger due t the irregular flw f air and the vibratins f the helicpter mtr. The digital reading always jumped abut s I was nly able t btain a reliable value with an uncertainty f ±0.1 g, s I used this precisin fr my experiment. The strbe light frequency was abslute with the least cunt f ±0.1 Hz. Here is my data. Page 4 Physics teacher supprt material 4

5 Data Set 1, Basic Data The mass f the helicpter and the wd munt was a cnstant mass f g. The rtr was started at the lwest pssible frequency, 74.1 Hz and increased t a maximum f 97.1 Hz. The crrespnding value f the scale measurements were recrded, and the lift mass was calculated simply as the ttal rest mass minus the reading mass: A Raw and prcessed data are presented in a clear and reasnable manner. Sme uncertainties are mentined in the text. m Lift = m Statinary m Frequency Data Set 2, Graphing Data Here is the data fr my graph: lift mass, frequency, and then frequency squared. EX The data cllectin, prcessing and graph are all relevant t the research questin. The standard f errr analysis is lw but the verall technique is mst apprpriate. A There are n uncertainties mentined here, and they are imprtant. Next I cnsider a graph 11 f frequency squared again mass lifted, as the riginal thery suggested. All the ther equatin values are cnstants. A The graph is relevant and apprpriately presented. Hwever, uncertainty bars are missing. Apparently the cmputer generated the gradient and y-axis intercept but these are nt shwn. Page 5 Physics teacher supprt material 5

6 Lking at my graph it is clear that the square f frequency is related t the lift mass. The graph line is reasnably understd as being linear because it tuches all the data pints in a straight line, and it tuches the riginal s I can say the relatinship is als prprtinal. The cmputer said that the gradient was ± Hz 2 / g. This means my cnclusin is justified t. My teacher said this errr f abut 3% was nt bad at all, given the uncertainties, s I am happy with my results. The thery is crrect. Imprvements and extensin ideas include the fllwing: EV Althugh the student is crrect here, mre thught and detailed appreciatin is expected fr a cnclusin. A The data is gd but mre detail is expected in an IA. Fr instance, the ffset f the zer-zer rigin and the uncertainty there wuld have helped establish a prprtinal relatinship. A The student appreciates the quality f the revealed relatinship with the calculatin f uncertainty here, presumably based n the standard deviatin f all the data pints and the best straight line. EV This errr, r rather uncertainty, is indeed gd. Given the data, methd and materials, perhaps it is even excellent. The frequency range f pssible lift values was limited by the remte cntrl. Perhaps a mre pwerful pwer supply wuld allw me t extend the range but I wuld nt want t burn ut the mtr. The cnstant vibratin f the helicpter n the balance and the variatin f air currents restricted the precisin f mass life measurements. Perhaps a smth running mtr culd be munted n the blck and then higher quality data with a wider range f values culd be btained. EV We knw nthing f the thery, nly that the given equatin is apprpriate fr the limited data range. Mre physics cntext wuld have helped here. It is hard t find any justificatin here, ther than gd quality data n the graph. Mre depth is required fr a justificatin. EV The student s brief cmments here are apprpriate, althugh the wind pwer extensin means nthing as it stands. If I had mre time I wuld repeat the experiment several times and take an average, but I ran ut f time as my teacher said I played arund t much with the helicpter and there was n mre class time t wrk n the IA. A further investigatin r extensin wuld include the study f wind pwer generatrs. Overall I enjyed wrking with the ty helicpter, especially just flying it abut the physics lab. Perhaps sme day I will be a pilt. Page 6 Physics teacher supprt material 6

7 FOOTNOTE REFERENCES (1) The ty helicpter is an AH-64 Apache Havc TM made by Air Hgs RC. (2) There are several surces f this infrmatin. See Wayne Jhnsn, Helicpter Thery (Dver Bks, 1994), the web site: dynamics.pdf as well as the article Investigating Flight with a Ty Helicpter by Michael Liebl, The Physics Teacher, Vlume 48, Octber 2010, pages (3) Fr much mre histry abut this see the web article: (4) Page 25 in Helicpter Thery (Dver Bks, 2012) by Wayne Jhnsn (5) (6) (7) See the nline Rtrcraft Flying Hanbk at: (8) The ty helicpter is an AH-64 Apache Havc TM made by Air Hgs RC. It runs n a rechargeable battery and is cntrlled by an infrared remte cntrl unit. See che-havc-heli-indr-infrared-micr-helicpter/ (9) (10) (11) My graph was made using LggerPr V sftware frm Vernier, see: Page 7 Physics teacher supprt material 7