Solving solid cylindrical projectile of various lengths Projectile: radius is 2.25mm length varies: 1,3, 5, ... up to maximum length of 41mm Coil: 20mm long 3mm inside radius 6mm outside radius Note: In Excel click on Data... Get External Data... Import text file... then choose this text file (projectile_length_results.txt) and click Finish. This data is tab delimited which is its default import format. Projectile length 1 mm Volume 31.8086256166875 mm3 -40 -0.005421480523899422 -39 0.01156355424907771 -38 -0.03694861249247818 -37 -0.01334598631899126 -36 -0.04598744810037495 -35 -0.008343863660334671 -34 -0.01721800366057838 -33 0.01993391158530301 -32 -0.01474282379115822 -31 -0.006904514240544362 -30 0.0003262305874146367 -29 0.0001459150928371021 -28 0.02410433056357793 -27 0.003728909598652831 -26 0.04765705252339718 -25 0.01215810827907493 -24 0.042944312454725 -23 0.0003835799686124886 -22 0.03750312418442185 -21 -0.02523673402712276 -20 0.005156626279610549 -19 0.04930466998735327 -18 0.03797085249491877 -17 0.007750429844431584 -16 0.04849671625866235 -15 0.09766674605682206 -14 0.1656476838997381 -13 0.2148260977437815 -12 0.362873866994587 -11 0.555636389547972 -10 0.7180223469810771 -9 0.6793514255366042 -8 0.5960522588840639 -7 0.4806352635936338 -6 0.3636609094669693 -5 0.2389230119208544 -4 0.1775000855572106 -3 0.1924494768297066 -2 0.08410611978840371 -1 0.06845353467980532 Projectile length 3 mm Volume 63.617251233375 mm3 -40 -0.03064441340458652 -39 0.0177002672642981 -38 0.01563428247903217 -37 -0.01917621890919453 -36 -0.02046883477164275 -35 -0.0262668321076204 -34 0.01921244225549293 -33 0.0369321697449001 -32 -0.03610373314363351 -31 0.02148550606749806 -30 0.01628551359679139 -29 0.006750858804232401 -28 0.0206509778089977 -27 0.0463810556004941 -26 -0.01458534978875428 -25 -0.007472619542082339 -24 0.005400883975433443 -23 0.0473833909900198 -22 0.02675977386053611 -21 -0.03158736295770231 -20 -0.02685801284686537 -19 0.02805976504213158 -18 0.08498374630368684 -17 0.1048914951294991 -16 0.20422717139566 -15 0.3413757327869888 -14 0.5287980460511554 -13 0.8785724711110925 -12 1.539265311307161 -11 2.572334496037602 -10 3.620406799020502 -9 3.742838255715505 -8 3.221900189455348 -7 2.446192407040036 -6 1.824055337001393 -5 1.275272303462484 -4 0.9718972240986786 -3 0.6443812048492064 -2 0.365964353006921 -1 0.1790114805709561 Projectile length 5 mm Volume 95.42587685006251 mm3 -40 0.01030232726970988 -39 0.01385844142845042 -38 -0.01986910357213731 -37 0.00865955746846336 -36 -0.01670967277171227 -35 0.01184363088183118 -34 0.02601175276643603 -33 0.007072161794371741 -32 0.009088677225180098 -31 0.009105700644601396 -30 0.009729747822309778 -29 0.007767935783384536 -28 0.002851851444553445 -27 -0.02373088265339279 -26 0.0282559135565512 -25 -0.01624959920837353 -24 -0.01681557680869472 -23 0.03512675251016386 -22 -0.02312982826682535 -21 0.04326747059967021 -20 0.02702869003794765 -19 0.1033751166235625 -18 0.1548633790062372 -17 0.2604605017984952 -16 0.4428053602589703 -15 0.7189971971253873 -14 1.284057083500252 -13 2.283523677862925 -12 3.993458905450398 -11 6.031346013218416 -10 7.656994042528674 -9 7.937857716744096 -8 6.719575014984121 -7 5.095441029819815 -6 3.64107162842066 -5 2.540844174493633 -4 1.753351218824352 -3 1.198849373681713 -2 0.7005807737087706 -1 0.322378328061569 Projectile length 7 mm Volume 127.23450246675 mm3 -40 0.01221850838048512 -39 -0.01907300277178293 -38 0.00907305574682957 -37 -0.01937879161712646 -36 0.0252894744114414 -35 0.004647193952805511 -34 0.007882058723500852 -33 -0.0003668655948299614 -32 0.01052688282679517 -31 -0.009736338949769966 -30 -0.003859450949072183 -29 0.04309192549125052 -28 -0.02947644489274724 -27 -0.007540203977336082 -26 -0.0007617099488416 -25 0.01199142790136096 -24 0.03935007413107258 -23 0.0285429802581106 -22 0.01929438157507508 -21 0.06460115213206205 -20 0.1360498185851783 -19 0.2153507955227613 -18 0.3241766898558656 -17 0.5542631391300471 -16 0.9035198188371724 -15 1.548202826395566 -14 2.808364115229225 -13 4.956711253609707 -12 7.732042288518353 -11 10.03264802519384 -10 10.77636483555391 -9 10.53165919834592 -8 9.518069710190275 -7 7.828640174894653 -6 5.721000464621942 -5 4.021962347230407 -4 2.752634555074454 -3 1.81505533550565 -2 1.172039930105568 -1 0.5095350575262911 Projectile length 9 mm Volume 159.0431280834375 mm3 -40 -0.01529308824421457 -39 0.009429490262364124 -38 -0.01874406596662217 -37 0.02329960348101148 -36 -2.382073587671538e-006 -35 0.005929767862263522 -34 0.01970044090409353 -33 0.01210671149114529 -32 -0.002963266037900414 -31 0.008840889704648124 -30 0.04229199296571898 -29 0.01384077082978419 -28 0.0320881725494838 -27 0.004094766831633839 -26 0.01002572672657312 -25 0.01359390923117686 -24 0.02241334418472618 -23 0.0117810786767223 -22 0.05876435501648987 -21 0.1552808632656076 -20 0.21064030385866 -19 0.3676395208409852 -18 0.6113661079202094 -17 1.035500571252818 -16 1.79290294770561 -15 3.187526279657534 -14 5.664672375011842 -13 8.837244859868253 -12 11.29555750958867 -11 12.23589623050544 -10 12.47900014806751 -9 12.27570523611473 -8 11.57119721693844 -7 10.34821073099439 -6 8.239564422574869 -5 5.913562732325162 -4 4.08815113115151 -3 2.733589650681584 -2 1.596688655174402 -1 0.8147329439106192 Projectile length 11 mm Volume 190.851753700125 mm3 -40 0.009331470555946572 -39 -0.01857365418390711 -38 0.01839678218581402 -37 0.003818004430528045 -36 -0.001913208944235924 -35 0.01919607612970993 -34 0.00965230260938162 -33 0.01590415113592867 -32 0.01565015870180186 -31 0.04591850204689801 -30 0.01511571709367898 -29 0.04066906268425501 -28 0.00734514602362886 -27 0.01576526391610753 -26 -0.002436170488330836 -25 0.01932493451390644 -24 0.02487169092701029 -23 0.09660213895010134 -22 0.1628099075204958 -21 0.2435455547270815 -20 0.4423195504496129 -19 0.6869419230949837 -18 1.154039072334715 -17 1.974074048598694 -16 3.509150393834447 -15 6.186674533670596 -14 9.607015662966077 -13 12.02892953453849 -12 13.06176275052587 -11 13.56689711285018 -10 13.73120294392262 -9 13.54598964686714 -8 13.01763765691969 -7 12.08782913306487 -6 10.59067167528789 -5 8.3030602836005 -4 5.875697659162375 -3 3.899532033870869 -2 2.347177836292917 -1 1.044540476077727 Projectile length 13 mm Volume 222.6603793168125 mm3 -40 -0.0068604315765757 -39 0.0287989340336607 -38 0.0121396921556738 -37 -0.0003554168965179472 -36 -0.01225163376749269 -35 0.03222711490508012 -34 0.02894364704180525 -33 0.02777518365825609 -32 0.01866145210933421 -31 0.002398214379124487 -30 0.01182637696799761 -29 0.0110854542926276 -28 0.02815422504955738 -27 0.009686586226858238 -26 0.01759037850303579 -25 0.03394873624982973 -24 0.1125656504861263 -23 0.181389056578547 -22 0.2743826838986428 -21 0.4360989856783326 -20 0.7435925195793175 -19 1.22690956273672 -18 2.104006814322252 -17 3.729210407127591 -16 6.606328457088639 -15 10.15270818149114 -14 12.48285651404812 -13 13.5850424958168 -12 14.21046214889031 -11 14.52241181754801 -10 14.59252711141254 -9 14.43165620428055 -8 13.9889386699521 -7 13.23262403705876 -6 12.16391846117124 -5 10.46166874663833 -4 8.105830492425813 -3 5.531473193840003 -2 3.36294545765417 -1 1.563968240908026 Projectile length 15 mm Volume 254.4690049335 mm3 -40 0.02387002934854852 -39 -0.009486807073986373 -38 0.02382848435476988 -37 0.0173813709988981 -36 0.02097580308764874 -35 0.01100032866419987 -34 0.006337163606332708 -33 0.04290867803823278 -32 -0.009984789525492794 -31 0.0288232892515851 -30 0.003354890042795306 -29 0.05732867048946698 -28 0.04277537740565967 -27 0.05312706932307448 -26 0.03012028028082631 -25 0.094433320039785 -24 0.2005586387049867 -23 0.2765265956313547 -22 0.4813933320074523 -21 0.7610479980512981 -20 1.285613771831274 -19 2.23348557161536 -18 3.89854235315616 -17 6.9155601247444 -16 10.56285657605685 -15 12.79031179158749 -14 13.93582941157447 -13 14.59973254208567 -12 14.99245973947736 -11 15.20492153108986 -10 15.21654677279483 -9 15.02666051836627 -8 14.6637978164006 -7 14.05909657296943 -6 13.21602047552251 -5 11.98632972660843 -4 10.11161349387327 -3 7.577541527730086 -2 4.767531793070738 -1 2.260329010497754 Projectile length 17 mm Volume 286.2776305501875 mm3 -40 -0.00082889388601358 -39 0.00482590192573615 -38 0.008613318841330118 -37 0.02253050492685123 -36 0.00131621925029016 -35 -0.002214159930866494 -34 0.04393640728542444 -33 0.01971122574967824 -32 0.03632726334254698 -31 0.005497532024022781 -30 0.02749810955765111 -29 0.06893937622502658 -28 0.04968228734141526 -27 0.03254666854854248 -26 0.1256106433772874 -25 0.2185508109386035 -24 0.3076211189307029 -23 0.4866795735947358 -22 0.8111997772747286 -21 1.336013695479775 -20 2.305991671095222 -19 4.116303143359801 -18 7.220300199862741 -17 10.86992973073176 -16 13.01154346716321 -15 14.16522927374965 -14 14.89013271686687 -13 15.32105860368616 -12 15.62534135289703 -11 15.71103047574218 -10 15.64899858378 -9 15.43400996354902 -8 15.08312941434146 -7 14.63002729845284 -6 13.88084317027831 -5 12.86006914133217 -4 11.39531093385364 -3 9.327098529480598 -2 6.507043770907361 -1 3.156731316702691 Projectile length 19 mm Volume 318.086256166875 mm3 -40 0.02891775171720304 -39 0.0229034066938809 -38 0.0168487333249622 -37 0.01289331469422514 -36 0.01654675588458427 -35 0.05011759036229113 -34 -0.01546811706384873 -33 0.04171808407841694 -32 0.0005775215154767304 -31 0.02500818906239026 -30 0.03867753747260825 -29 0.007793229676752921 -28 0.02210163286075914 -27 0.1382711410992078 -26 0.2167981405673222 -25 0.2934906475026259 -24 0.5475195832319943 -23 0.8641710170033649 -22 1.390633600418921 -21 2.425283863544566 -20 4.237996802737117 -19 7.4180319983358 -18 11.09212205192567 -17 13.17823858674285 -16 14.36347611267187 -15 15.07769902363515 -14 15.54667771589895 -13 15.86959559897044 -12 15.95754107776292 -11 16.02389456279634 -10 15.88792319051018 -9 15.71480049212097 -8 15.38565001762883 -7 14.92249457526361 -6 14.30564024295762 -5 13.34858441545299 -4 12.08814342949137 -3 10.33682956319207 -2 7.738476431666373 -1 4.21008649217738 Projectile length 21 mm Volume 349.8948817835625 mm3 -40 0.01426391171090954 -39 0.02019879100766531 -38 0.01253262853914542 -37 -0.005341620857860272 -36 0.01016675694163668 -35 -0.01790487415760959 -34 0.007982198920319377 -33 0.02390595763656265 -32 0.01105969613997703 -31 0.01125725049165835 -30 0.04616599605697998 -29 0.05034877131577773 -28 0.1132441456572395 -27 0.2349278187723065 -26 0.3377731966269136 -25 0.5242530379394547 -24 0.8778394132224167 -23 1.435267084297577 -22 2.488276429725177 -21 4.33863698010923 -20 7.600822742946467 -19 11.26486610701262 -18 13.307631202277 -17 14.47081339763895 -16 15.23496388063805 -15 15.73252290181552 -14 16.06670636222585 -13 16.2172657547036 -12 16.29735023049894 -11 16.24551423279903 -10 16.09974540217807 -9 15.90654731742624 -8 15.52958546796846 -7 15.07421462364334 -6 14.37573789266221 -5 13.46146721905941 -4 12.25493522619318 -3 10.49828507141865 -2 8.059158889119706 -1 4.645855647371721 Projectile length 23 mm Volume 381.70350740025 mm3 -40 0.02576532420617365 -39 0.01209798659295418 -38 -0.01432833586132595 -37 0.01724156308355984 -36 0.01992212610638305 -35 0.03153297166953479 -34 0.02001155419320942 -33 0.03619370823921202 -32 0.06996714447225537 -31 0.0152227047207775 -30 0.009187375621960264 -29 0.1496976664312849 -28 0.2324123481282358 -27 0.3415834101974415 -26 0.5312461186837604 -25 0.8766654003673139 -24 1.470524373537817 -23 2.519289103289432 -22 4.401886863527919 -21 7.726232248791059 -20 11.3731038443103 -19 13.41635819654364 -18 14.54771152556691 -17 15.32285926293145 -16 15.84103021510688 -15 16.18571885188667 -14 16.36575880035007 -13 16.4464009535954 -12 16.45224268589469 -11 16.36024576373903 -10 16.18514956431121 -9 15.88719780078028 -8 15.50859555515834 -7 14.99959358467196 -6 14.23477080959978 -5 13.28583834831676 -4 11.92708433853185 -3 9.991074592631122 -2 7.325041797841528 -1 3.80901536859885 Projectile length 25 mm Volume 413.5121330169375 mm3 -40 0.01722263775353747 -39 0.01873364363782918 -38 0.05195202931740401 -37 -0.01366037333754037 -36 0.04139879268690146 -35 0.01696218131382504 -34 0.07376106090554868 -33 0.0847841809087726 -32 0.08669511783391246 -31 0.09675515934062968 -30 0.11204138337011 -29 0.2432609359698391 -28 0.3434577609841121 -27 0.5351317332217285 -26 0.9244389967460159 -25 1.521152979853991 -24 2.559025203263813 -23 4.556464314094594 -22 7.859270973093478 -21 11.48821627658515 -20 13.4931722213202 -19 14.63528948504471 -18 15.42082444379217 -17 15.93331242856785 -16 16.30335647536244 -15 16.51102948396589 -14 16.58113954226187 -13 16.60835047385438 -12 16.54013498272055 -11 16.42034242457606 -10 16.15048940509417 -9 15.85004452742659 -8 15.34207565792531 -7 14.75265932117232 -6 13.89528217640013 -5 12.71395785438079 -4 11.02352553743432 -3 8.780132549725245 -2 5.75105622948348 -1 2.720385271993321 Projectile length 27 mm Volume 445.320758633625 mm3 -40 -0.01305413751934724 -39 0.04749071951529583 -38 0.01892262932093308 -37 0.02871118505205785 -36 0.0226900231271218 -35 0.01843983342935125 -34 0.07301651130611936 -33 0.08412262422797208 -32 0.05441519254866899 -31 0.1375411954929441 -30 0.2523792407087002 -29 0.353053965366017 -28 0.6062552254256933 -27 0.9498293945648916 -26 1.531700582708569 -25 2.630819896379094 -24 4.615227691221058 -23 7.982050101113031 -22 11.56295478976982 -21 13.54477795193454 -20 14.70443918658432 -19 15.463909784281 -18 16.00678083096615 -17 16.34155094652865 -16 16.54774896737795 -15 16.68949355682457 -14 16.72049872484903 -13 16.67869922510824 -12 16.54969890022682 -11 16.34588363397642 -10 16.05901391059594 -9 15.64778564476006 -8 15.03278178540023 -7 14.29858378714142 -6 13.20981021930758 -5 11.60168093415766 -4 9.580129894917931 -3 6.778990286374274 -2 4.125389166253095 -1 1.910366665459282 Projectile length 29 mm Volume 477.1293842503125 mm3 -40 0.0593190583691532 -39 0.0316258378850944 -38 0.05098823673203949 -37 0.02450665259951147 -36 0.03310393612932361 -35 0.01605839853425109 -34 0.1112997910353393 -33 0.065215508545284 -32 0.1709502967325548 -31 0.2425708517665324 -30 0.3906775752654643 -29 0.6114540396344079 -28 0.9717564199655118 -27 1.579166595493762 -26 2.673187377644093 -25 4.691320903715893 -24 8.093717448457722 -23 11.64953010165073 -22 13.5888160911103 -21 14.77110781052144 -20 15.55042977601349 -19 16.04573550170846 -18 16.45733723019662 -17 16.60252631823763 -16 16.79880080555455 -15 16.81154204632616 -14 16.76351818322591 -13 16.64098330736644 -12 16.4824834971997 -11 16.2268866934148 -10 15.81869232422487 -9 15.2545867361751 -8 14.51625582519509 -7 13.50688325989428 -6 11.99930735353794 -5 10.04917076579382 -4 7.34985099754564 -3 4.925492221038605 -2 2.967294042550808 -1 1.399714651146722 Projectile length 31 mm Volume 508.938009867 mm3 -40 -0.01135311958091977 -39 0.04826183538658998 -38 0.03067391284302792 -37 0.03364513940594384 -36 0.01198466854129936 -35 0.07054985440134663 -34 0.03664198856022563 -33 0.1335929260613194 -32 0.2419360180441705 -31 0.3808108551391467 -30 0.6181625382799196 -29 0.9568842665420009 -28 1.573292878956425 -27 2.673259877970531 -26 4.745715893112704 -25 8.146099893676597 -24 11.71354621970712 -23 13.63803882302208 -22 14.80904446880128 -21 15.57416174545294 -20 16.1061818139481 -19 16.50937105256195 -18 16.70587556005239 -17 16.8586957338015 -16 16.89665828454228 -15 16.86101936348549 -14 16.74709843448687 -13 16.57907768289296 -12 16.32149094298366 -11 15.95460670610358 -10 15.40653064395974 -9 14.71128515856404 -8 13.71038348088525 -7 12.2466090052243 -6 10.36733766748336 -5 7.724582618817133 -4 5.36499229316213 -3 3.546740029173466 -2 2.165607261254412 -1 1.008375227915578 Projectile length 33 mm Volume 540.7466354836876 mm3 -40 0.04126997813292902 -39 0.03205702915440495 -38 0.02089158458234046 -37 0.06471774759930764 -36 0.04863348861123761 -35 0.08383339350216891 -34 0.1649131364080938 -33 0.260026534484438 -32 0.3889829845663139 -31 0.6125773294361323 -30 1.003541447643521 -29 1.614475131005334 -28 2.746975442694604 -27 4.804078714396527 -26 8.218988266279885 -25 11.7504058249425 -24 13.68270780703289 -23 14.84628167670522 -22 15.65025904873206 -21 16.16097503004731 -20 16.52276961321084 -19 16.7584246092577 -18 16.91065316348405 -17 16.9161245827172 -16 16.91225302524809 -15 16.85091643010937 -14 16.65034976604936 -13 16.4172016171086 -12 16.04051530281679 -11 15.53034575498058 -10 14.84714344007839 -9 13.88042437333595 -8 12.41318123175445 -7 10.45462269099016 -6 8.025362694214044 -5 5.675641430432418 -4 3.914616881449725 -3 2.644652850480849 -2 1.621195095581363 -1 0.7639447363864076 Projectile length 35 mm Volume 572.555261100375 mm3 -40 0.0252428959490213 -39 0.03925011219384618 -38 0.03683176192798546 -37 0.06390363032309028 -36 0.06397977433100167 -35 0.172413601119839 -34 0.2506327016292884 -33 0.3984568674033381 -32 0.6607821000956204 -31 1.035994085549382 -30 1.642740707088049 -29 2.772180600789786 -28 4.863977701741129 -27 8.28707036689006 -26 11.78155563115541 -25 13.69294099023294 -24 14.86534973296391 -23 15.66315153619795 -22 16.19478298248345 -21 16.57780667958712 -20 16.79210685146802 -19 16.94854083418867 -18 16.98321183021614 -17 16.92110519628644 -16 16.87484356606984 -15 16.72442728873768 -14 16.49350011997894 -13 16.12793868404575 -12 15.65493342588872 -11 14.92265278677954 -10 13.98968422467789 -9 12.56309425300211 -8 10.71423472524514 -7 8.181487255533392 -6 5.907988371267847 -5 4.210291837680213 -4 2.942520185538404 -3 2.003597784847794 -2 1.243843646191228 -1 0.5872926422405802 Projectile length 37 mm Volume 604.3638867170625 mm3 -40 0.05316934255984734 -39 0.07135699205619224 -38 0.08134719282457657 -37 0.11502400001126 -36 0.1867200684972063 -35 0.288781904145161 -34 0.3885593059923522 -33 0.6541154696268469 -32 1.014728171669038 -31 1.663451079116486 -30 2.80245406114578 -29 4.907303968589035 -28 8.312307093131707 -27 11.81946181355035 -26 13.72448605635526 -25 14.89787133124299 -24 15.70352351891836 -23 16.21589532054523 -22 16.62517794698962 -21 16.80880657982583 -20 16.94317057057963 -19 17.00513055089773 -18 17.0174220220012 -17 16.955976627957 -16 16.7457096045212 -15 16.53823975776549 -14 16.19488138723639 -13 15.70797384782852 -12 15.01275158419812 -11 14.04903322325998 -10 12.66565975187583 -9 10.80008549218382 -8 8.312991136763518 -7 6.011312329706351 -6 4.338488391233415 -5 3.179459767912868 -4 2.275472940961077 -3 1.560308632862162 -2 0.9782168750568787 -1 0.4556631750627227 Projectile length 39 mm Volume 636.17251233375 mm3 -40 0.04105751903237932 -39 0.1032558964401083 -38 0.06527574136604354 -37 0.1709193035400128 -36 0.2718525876362845 -35 0.3760173183379319 -34 0.6543144362657639 -33 1.038669701358493 -32 1.683379858555535 -31 2.838510820174832 -30 4.943422811734733 -29 8.368615859035435 -28 11.84875440168962 -27 13.73891121370658 -26 14.91253332749166 -25 15.72766616745596 -24 16.24518230017738 -23 16.62454209397717 -22 16.8537651062202 -21 17.00310540708093 -20 17.04266376707007 -19 17.03693955076628 -18 16.96972704877019 -17 16.81543861430778 -16 16.57840004099678 -15 16.23630483916348 -14 15.7819937265998 -13 15.08531714877559 -12 14.14458970084959 -11 12.72947572554912 -10 10.90966629210823 -9 8.473859578154254 -8 6.178097563789795 -7 4.50943031405293 -6 3.330541304345553 -5 2.451010557073015 -4 1.790558536010487 -3 1.21843044581896 -2 0.7676180210501675 -1 0.3893273808791284