ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAFAGAHAIAJAKALAMANAOAPAQARASATAUAVAWAXAYAZBABBBCBDBEBFBGBHBIBJBKBLBMBNBOBPBQBRBSBTBUBVBWBXBYBZCACBCCCDCECFCGCHCICJ
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INVERSE SQUARE TABLE FOR ALL Xs
Len Joeris, October, 2017
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Design Forces on legs (in gr) at 15kg load
Leg Testing Lengths - BS varies within a stick; we want to test at length close to in-place length (L)- USE L +2cm cm x
0.393701#NAME?
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(fm tab Leg Forces Based on Dimensions)w/ Safety FactorsUSE
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MIN0.060.1Design L (cm)
L(cm)+2 ininches
for testEffective Length (EL) FactorSection 2 - Effective Length factor calculation
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B-Base40904335449927.0511.412CONSERVATIVELessEven LessThese are back-calculated/'reverse engineered from data obtained on stick weights, 36" SFPD measured BS, and bracing interval from a successful all Xs tower (in another State)
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C-Base42724528469922.559.710
(26.5 got to 100%)
conservativeConservative
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B-Chim37513976412625.40310.811USEAssumed(26 got to 100%)(25 got to 100%)the specific data used was that C-tower legs braced at a 1/11th interval held full load, and measured SFPD BS at 36" was "between 25 and 26.5 grams"
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C-Chim37503975412540.40216.7170.5460.53750.5460.568INVERSE SQUARE TABLES FOR LADDER WOOD
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SFPD (single finger push-down value) BS
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Test Length1/[prop(of 36)^2]
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NOTE: !!!at 10"12.96168.5180.8183201.5226.8234.6246.2249.5260.5270.1272.2286.8290.3294.2298.1304.6311317.5322.7330.5337343.4349.9359362.9374.5375.8382.3388.8395.3401.8408.2414.7421.2427.7434.2440.6447.1453.6460.1466.6473479.5486492.5499509.7511.9518.4524.9531.4537.8544.3550.8560.1563.8570.2576.7583.2589.7596.2602.6609.1615.6622.1110.2116.6123.1129.6136.1142.6149155.5162168.577.890.7103.7116.6
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THIS ROW DRIVES ALL OTHER BS ENTRIES BELOWat 11"10.711139.2149.4151.2166.6187.4193.9203.5206.2215.3223.2224.9237239.9243.1246.3251.7257.1262.4266.7273.1278.5283.8289.2296.7299.9309.5310.6316321.3326.7332337.4342.7348.1353.5358.8364.2369.5374.9380.2385.6390.9396.3401.7407412.4421.3423.1428.4433.8439.1444.5449.9455.2462.9465.9471.3476.6482487.3492.7498503.4508.8514.19196.4101.8107.1112.5117.8123.2128.5133.9139.264.37585.796.4
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at 12"9117125.6127.1140157.5162.9171173.3180.9187.6189199.2201.6204.3207211.5216220.5224.1229.5234238.5243249.3252260.1261265.5270274.5279283.5288292.5297301.5306310.5315319.5324328.5333337.5342346.5354355.5360364.5369373.5378382.5389391.5396400.5405409.5414418.5423427.543276.58185.59094.599103.5108112.511754637281
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Section 1- Forces on legs (at a 15kg tower load)at 17"4.48458.362.663.369.778.581.285.286.390.193.594.299.2100.5101.8103.1105.4107.6109.9111.7114.4116.6118.8121.1124.2125.6129.6130132.3134.5136.8139141.3143.5145.7148150.2152.5154.7157159.2161.4163.7165.9168.2170.4172.7176.4177.1179.4181.6183.9186.1188.3190.6193.8195.1197.3199.6201.8204206.3208.5210.8213215.338.140.442.644.847.149.351.653.856.158.326.931.435.940.4
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These come from a separate table- the force on one leg is 1/4 of the loadat 36"11313.9514.1215.5517.518.11919.2520.120.842122.1322.422.72323.52424.524.925.52626.52727.72828.92929.53030.53131.53232.53333.53434.53535.53636.53737.53838.539.3339.54040.54141.54242.543.2243.54444.54545.54646.54747.54853.58.599.51010.51111.51212.5136789
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on the tower, times 1 over the cosine of the angle it is leaning in at.at 48"0.5637.37.87.98.79.810.210.710.811.311.711.812.412.612.812.913.213.513.81414.314.614.915.215.615.816.316.316.616.917.217.417.71818.318.618.819.119.419.72020.320.520.821.121.421.722.122.222.522.823.123.323.623.924.324.524.82525.325.625.926.226.426.7274.85.15.35.65.96.26.56.877.33.43.94.55.1
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example- C base leg angle= 28.61 degrees; COS of 28.61= 0.8779; 1/0.8779= 1.1391. 1.1391 x 3750 (which is 1/4 of 15000gr)= 4272grSection 3 - (calculated) buckling strength (BS) at different stick lengths given a 36" SFPD measurementThe values in ROW 15 drive the table below and alternate length values in this table. You can change value in row 15 for any measured BS you want to see inverse square values
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Section 4- The actual inverse square tablesThis is simply an inverse square calculation (the relationship of BS to length). The values in column G are 1 divided by the proportion (of a 36" stick) squared; example- the 24" value is 1/(24/36)2, which = 2.250CBB & C
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Braced segment in-place BS (given measured 36" BS & EL factor)In other words, if you measure BS at 36 inches, what will it measure at different lengths, assuming the exact same inherent BS in lengths/cases. Measuring at shorter length gets you more precise/accurate measurement.BS needed approx=21501700(fm Structural Analysis Notebook)BS needed approx=1500maybe a bit less
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Base and Chimney legs below-ladders to the right side of table36" values from aboveNOTE- Using 13 gr SFPD as lower limit- this is approx 0.8gr (for 36" 1/8 x 1/8), which is$4.25 PER STICKfrom Specialized Balsa; a practical limit. 0.7gr/36is $6.95 per stickLower BS values than left side- FOR LADDER AT TOP OF BASEEven lower values for ladder at top of tower
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CB 1/6BB 1/7BB 1/6CB 1/5BB 1/5CB 1/4BB 1/4CB 1/3
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BASE LEGSL (in cm)
Proportion of test length (91.6)
1/prop236" SFPD1313.9514.1215.5517.518.11919.2520.120.842122.122.422.72323.52424.524.925.52626.52727.72828.92929.53030.53131.53232.53333.53434.53535.53636.53737.53838.539.3339.54040.54141.54242.543.2243.54444.54545.54646.54747.54853.58.599.51010.51111.51212.51367890
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36"91.611
36" SFPD x EL factor
7.17.67.78.59.69.910.410.51111.411.512.112.212.412.612.813.113.413.613.914.214.514.715.115.315.815.816.116.416.716.917.217.517.71818.318.618.819.119.419.719.920.220.520.72121.521.621.822.122.422.722.923.223.623.82424.324.624.825.125.425.725.926.229.24.64.95.25.55.766.36.66.87.13.33.84.44.9
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C-DIV Leg22.550.24616.5117126127140158163171173181188189199202205207212216221224230234239243250252260261266270275279284288293297302306311315320324329333338342347354356360365369374378383389392396401405410414419423428432482
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B-DIV Leg27.050.29511.4781878897110113119121126130131139140142144147150153156160163166169173175181182185188191194197200203207210213216219222225229232235238241246247250254257260263266271272275279282285288291294297301335
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12"30.530.3339646969768689939599102103109110112113115118120122125128130133136138142143145147150152155157160162165167170172174177179182184187189193194197199201204206209212214216219221224226229231233236263
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10"25.440.27812.969299100110124128134136142147149157159161163166170173176180184188191196198205205209212216219223226230234237241244248251255258262265269272278280283287290294297301306308311315318322326329333336340379
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C-DIV Leg22.550.24616.5163171173181199202212224230243250260261270275284293297302306311315320329333338342347354356360365369374378383389392396401405410414419423428432482
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1/37.5170.082148.5105411311145126114191468154115611630169017031794181618411865190519461987201920682108214921892246227023432351239224332473251425542595263526762716275727972838287829192960300030413081312231893203324332843324336534063446350435273568360836493689373037703811385138924338
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1/45.6380.062264.01187420112035224225232609273927752897300430273190322932723315338734603532358936763748382038923993403641664180425243244397446945414613468547574829490149735045511751895261533354065478555056695694576658385910598260546126623062706343641564876559663167036775684769197712
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1/54.510.049412.51292831423180350239424077427943364527469447304984504551135180529354065518560857435856596960816239630765096532664467576870698270957207732074337545765877717883799681088221833484468559867188588897900991229235934794609572973597989910100231013510248103611047310586106991081112050
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1/63.7580.041594.0242164524458050435676
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Ladder at top of base(5/32)
same B & C4.710.051378.221755185919622065216822722375247825812685
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36
B-DIV Leg27.050.29511.4781878897110113119121126130131139140142144147150153156160163166169173175181182185188191194197200203207210213216219222225229232235238241246247250254257260263266271272275279282285288291294297301335
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1/46.760.074183.47130213971415155817531813190319282014208821042217224422742304235424042454249425552605265527052775280528952905295530053055310531563206325633063356340634563506355636063656370737573807385739403957400740574107415742074258433043584408445845084558460846584708475848095359
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1/55.410.059286.68203521842210243427392833297430133146326232873464350635533600367837573835389839914070414842264336438345244539461846964774485249315009508751655244532254005478555756355713579158705948602661566183626163396418649665746652676568096887696570447122720072797357743575138374
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1/64.510.049412.82293031443183350539444080428343394531469747334988504951175184529754105522561257485860597360866244631165146537664967626875698771007213732574387551766477767889800281148227834084528565867888658903901691299241935494679579974298059918100301014310256103681048110594107061081912059
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1/73.860.042561.8939884280433247715369
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THESE VALUES ARE
1/8-36"STICK WGT(Gr)For Trendline0.750.770.890.911.111.191.553.433.513.533.663.733.783.841.83.933.933.933.843.843.843.843.843.843.84B & C
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DRIVEN FROM THE
= Gr/cm0.00820.00840.00970.00990.012100000.013000000000000000000000000.01690000.03740.03830.03850.040.04070.04130.04190.01970.04290.04290.04290.04190.04190.04190.04190.04190.04190.0419BS needed approx=1500maybe a bit less
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COMPARISON1/8-36"STICK WGT(Gr)0.630.650.80.840.971.041.361.6
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TABLES BELOW= Gr/cmFor Best0.00690.00710.00870.00920.01060.0114000000000000000000000000.014800000000000.017500000000
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For all 4 legs:108.2cm= Leg weight of1.691.7322.0500000000002.500002.68000000000000000000000003.490007.727.97.958.248.48.518.644.058.858.858.858.648.648.648.648.648.648.64Even lower values for ladder at top of tower
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90.2cm2.012.062.382.4400000000002.9700003.1900000000000000000000
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BC 1/6CC 1/9CC 1/8BC 1/5CC 1/7BC 1/4CC 1/6
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CHIMNEY LEGSL (in cm)
Proportion of test length (91.6)
1/prop236" SFPD131414.115.5517.518.11919.320.120.82122.1322.422.72323.52424.524.925.52626.52727.72828.92929.53030.53131.53232.53333.53434.53535.53636.53737.53838.539.3339.54040.54141.54242.543.243.54444.54545.54646.54747.54853.56789
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36"91.611
36" SFPD x EL factor
7.17.67.78.59.69.910.410.51111.411.512.112.212.412.612.813.113.413.613.914.214.514.715.115.315.815.816.116.416.716.917.217.517.71818.318.618.819.119.419.719.920.220.520.72121.521.621.822.122.422.722.923.223.623.82424.324.624.825.125.425.725.926.229.23.33.84.44.9
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C-DIV Leg40.4020.4415.14363940444951535456585962636465666769707273747678798181838486878890919394959798100101102104105107108110111112114115116118119121122123125126128129131132133135150
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B-DIV Leg25.4030.277139299100110124128135137143148149157159161163167170174177181185188192197199205206209213217220224227231234238241245248252256259263266270273279280284288291295298302307309312316319323327330334337341380
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11"27.990.30610.7176828391102106111113118122123129131133135137140143146149152155158162164169170173175178181184187190193196199202205208211213216219222225230231234237240243246249253254257260263266269272275278281313
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17"43.26
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C-DIV Leg40.4020.4415.14363940444951535456585962636465666769707273747678798181838486878890919394959798100101102104105107108110111112114115116118119121122123125126128129131132133135150
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1/58.080.088128.5191297999110911228127013331351141014621473155315721593161416491684171917471789182418591894194419652028203520702105214021752210224522802315235123862421245624912526256125962631266627012760277228072842287729122947298230333052308731223157319232283263329833333368
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1/66.7340.074185.0513131409142715711768182919201945203121062122223622632294232423742425247525162576262726772728279928292920293029813031308231323183323332843334338534353486353635873637368837383789383938903974399140414092414341934244429443674395444644964547459746484698474947994850
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1/75.7720.063251.8717881918194221382407248926132647276428662888304330813122316332323301336934243507357636443713380938513974398840574126419442634332440144694538460746764745481348824951502050885157522652955409543255015570563857075776584559445982605161206189625763266395646465326601
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1/85.050.055328.9823352506253627933143325134133458361037433772397540244077413142214311440144734580467047604850497650295191520952995389547855685658574858385928601761076197628763776466655666466736682669157065709571857275736474547544763477637814790379938083817382638352844285328622
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1/94.4890.049416.362955317132103535397841154319437645694738
60
61
62
B-DIV Leg25.4030.277139299100110124128135137143148149157159161163167170174177181185188192197199205206209213217220224227231234238241245248252256259263266270273279280284288291295298302307309312316319323327330334337341380
63
1/38.470.092117.0283189190299411181156121412301284133213421414143114501470150115331565159116291661169317251770178918471853188519171949198120132045207721082140217222042236226823002332236423962428246025132524255625882620265226842715276127792811284328752907293929713003303530673418
64
1/46.350.069208.04147715851604176619882056215821872283236723852514254425782613266927262783282828972953301030673146318032833294335134083464352135783635369237483805386239193976403240894146420342604316437344674487454446004657471447714828490949414998505551115168522552825339539554526077
65
1/55.080.055325.06230724762506276031063212337234173567369937273928397640294082417142604348441945264615470347924916496951295147523653245413550255915679576858575946603461236212630163896478656766566744683369807011709971887277736574547543767177207809789879878075816482538342843085199495
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1/64.230.046468.0833223565360939744473462648564920513753265367565657255802587860066134626263646517664567736900707971567386741275397667779579238051817883068434856286908817894590739201932894569584971298401005210095102231035110479106061073410862110461111711245113731150111629117561188412012121401226813673
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1/73.630.04637.114522485349125409608862966609669669927249
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THESE VALUES ARE
1/8-36"STICK WGT(Gr)For Trendline0.750.770.80.850.890.910.940.951.111.171.191.31.412.933.013.081.553.243.293.373.433.513.533.663.733.783.843.933.843.843.843.84
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DRIVEN FROM THE
= Gr/cm0.00820.00840.00870.0093000.00970.0099000.01030.010400000000000.012100.012800000.01300000000.014200000000.015400000.0320.03290.03360.01690.03540.03590.03680.03740.03830.03850.040.04070.04130.04190.04290.04190.04190.04190.0419
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COMPARISON1/8-36"STICK WGT(Gr)0.630.650.70.750.80.840.830.840.971.021.041.131.251.36
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TABLES BELOW= Gr/cmFor Best0.00690.00710.00760.00820.00870.00920.00910.009200000000000.010600.011100000.011400000000.012300000000.0136000000.0148
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For all 4 legs:101.61cm= Leg weight of0.890.94000.991.01001.042.1400000000001.2301.300001.3200000002.9300000003.1700006.66.786.933.497.297.417.597.727.97.958.248.48.518.648.858.648.648.648.64
73
161.61cm1.411.5001.571.61001.662.5400000000001.9602.0600002.100000003.4800000003.780000
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100