Volume Verses Crank Angle

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MolaKule

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In this Question we will continue to use my 1999 S-10 engine (6-cylinder, 4.3L Vortec) as the question Example. Data: The total Displacement of the engine is 262.3 cubic inches. Bore is 4.012 inches, Stroke is 3.48 inches, and the Connecting Rod Length is 5.7 inches from center of Wrist-Pin bore to center of Bid-End bore. Just analyzing one cylinder, determine the volume of that one cylinder, in cubic inches, at a Crank Angle of 225 Degrees. This question is open to Everyone. Just remember folks, your response goes into a queue so if you don't see it right away, it is awaiting posting and will be posted if it is relevant to the question.
 
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Is your engine overbored? Stock bore on a GM 4.3 is 4.000". How is the 225 degree crank angle defined? Is that 225 degrees after TDC Firing or something else? Do you want the total volume of the cylinder, or just the volume remaining to be swept by the piston based on the crank angle?
 

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Originally Posted by A_Harman
Is your engine overbored? Stock bore on a GM 4.3 is 4.000".
Dimensions to be used in this problem are taken from the General Motors 4.3 L Powertrain Service manual, TP-6103.
Originally Posted by A_Harman
How is the 225 degree crank angle defined? Is that 225 degrees after TDC Firing or something else?
Quote
At 0 degrees Top Dead Center and at 180 degrees Bottom Dead Center, and with the crankshaft rotating clockwise, the piston motion is virtually zero.
Clockwise rotation of crankshaft is viewed as Clockwise rotation starting from 0.xxx degrees Top Dead Center, to 180 Degrees Bottom Dead Center, then back to 359.xxx degrees Top Dead Center.
Originally Posted by A_Harman
Do you want the total volume of the cylinder, or just the volume remaining to be swept by the piston based on the crank angle?
Hint: The cylinder volume at any point in time is solely a function of the crank angle at any point in time.
 
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MolaKule

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Originally Posted by SubieRubyRoo
32.7875 cubic inches. PFM if I get it right, cuz it was an educated guesstimate. Relegate me to the ranks of normal idjit if I guessed wrong. smile
A good start but not quite, so use your equations and keep cranking. smile
 
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My quick 6th grade math yielded 32.985 but I just woke up and may need to re-think my assumptions.
 

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A good start but not quite, so use your equations and keep cranking. The Volume HAS to be a function of (a result of) the crank angle in degrees or radians. HINT: The Volume of any one cylinder at a crank angle of 180 degrees or BDC is of course 1/6th the volume of 262.3 cubic inches. At any other crank angle, the volume of any one cylinder is less than 1/6th the volume of 262.3 cubic inches.
 
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Originally Posted by MolaKule
Originally Posted by A_Harman
Is your engine overbored? Stock bore on a GM 4.3 is 4.000".
Dimensions to be used in this problem are taken from the General Motors 4.3 L Powertrain Service manual, TP-6103.
Originally Posted by A_Harman
How is the 225 degree crank angle defined? Is that 225 degrees after TDC Firing or something else?
Quote
At 0 degrees Top Dead Center and at 180 degrees Bottom Dead Center, and with the crankshaft rotating clockwise, the piston motion is virtually zero.
Clockwise rotation of crankshaft is viewed as Clockwise rotation starting from 0.xxx degrees Top Dead Center, to 180 Degrees Bottom Dead Center, then back to 359.xxx degrees Top Dead Center.
Originally Posted by A_Harman
Do you want the total volume of the cylinder, or just the volume remaining to be swept by the piston based on the crank angle?
Hint: The cylinder volume at any point in time is solely a function of the crank angle at any point in time.
Yes it is, but there is the complicating factor of compression ratio, which requires you to take into account the clearance volume at the top of the stroke, not just the swept volume. Now we're getting into semantics. When you say "cylinder", do you mean a simple geometric cylinder, or an engine cylinder, which includes clearance volume? But anyway, I have a spreadsheet that does crank and slider calculations based on rod length, bore, stroke, deck height, piston compression height, etc, and puts out piston position, bore volume above the piston, piston velocity, piston acceleration, and cylinder wall thrust load in G's. Based on typical 350 Chevy engine dimensions, which I am pretty sure are the same as the 4.3 V6: DECK HGT= 9.025 STROKE= 3.48 PIST HGT= 1.56 ROD LENGTH= 5.7 BORE DIA= 4.000 R/L= 0.305263158 DECK CLR= 0.025 L/R= 3.275862069 Here are the piston travel and bore volume values: CRANK ANGLE PISTON TRAVEL VOLUME ABOVE (DEG) (IN. BELOW DECK) IN^3 0 0.025 0.314159265 1 0.025345903 0.318506008 2 0.026383439 0.331544068 3 0.028112091 0.353266949 4 0.030530997 0.383663825 5 0.033638953 0.42271955 6 0.03743441 0.470414665 7 0.041915477 0.526725415 8 0.047079923 0.591623756 9 0.052925176 0.665077379 10 0.059448328 0.747049726 11 0.066646134 0.837500014 12 0.074515012 0.93638326 13 0.083051053 1.04365031 14 0.092250014 1.159247867 15 0.102107328 1.283118527 16 0.112618103 1.415200814 17 0.123777124 1.555429218 18 0.135578863 1.703734236 19 0.148017473 1.860042419 20 0.161086799 2.024276413 21 0.174780379 2.196355015 22 0.189091448 2.376193219 23 0.204012945 2.563702274 24 0.219537512 2.758789742 25 0.235657506 2.961359555 26 0.252364997 3.171312079 27 0.269651778 3.388544179 28 0.287509369 3.612949288 29 0.305929022 3.844417478 30 0.324901728 4.082835528 31 0.344418221 4.328087007 32 0.364468985 4.580052347 33 0.385044264 4.838608924 34 0.406134062 5.103631147 35 0.427728156 5.374990533 36 0.449816099 5.652555807 37 0.472387228 5.936192985 38 0.495430674 6.225765467 39 0.518935366 6.521134138 40 0.542890041 6.822157458 41 0.56728325 7.128691568 42 0.59210337 7.440590387 43 0.617338606 7.757705721 44 0.642977007 8.079887362 45 0.669006467 8.406983203 46 0.695414739 8.738839341 47 0.722189443 9.075300196 48 0.749318073 9.416208615 49 0.776788008 9.761405994 50 0.804586519 10.11073239 51 0.832700782 10.46402664 52 0.861117884 10.82112648 53 0.889824835 11.18186866 54 0.918808574 11.54608906 55 0.948055983 11.91362284 56 0.977553894 12.28430453 57 1.007289101 12.65796816 58 1.037248366 13.03444738 59 1.067418432 13.41357561 60 1.097786031 13.79518612 61 1.128337897 14.17911219 62 1.15906077 14.5651872 63 1.189941412 14.9532448 64 1.220966612 15.34311896 65 1.252123198 15.73464416 66 1.283398044 16.12765547 67 1.314778085 16.52198869 68 1.346250318 16.91748043 69 1.377801819 17.31396829 70 1.409419747 17.71129089 71 1.441091356 18.10928806 72 1.472804 18.50780091 73 1.504545147 18.90667193 74 1.536302382 19.30574511 75 1.568063417 19.70486605 76 1.599816101 20.10388205 77 1.631548425 20.50264218 78 1.66324853 20.90099745 79 1.694904714 21.29880079 80 1.72650544 21.69590723 81 1.758039343 22.09217394 82 1.789495235 22.48746033 83 1.820862108 22.88162809 84 1.852129148 23.2745413 85 1.883285731 23.66606647 86 1.914321436 24.05607264 87 1.945226044 24.4444314 88 1.975989545 24.83101695 89 2.006602141 25.21570618 90 2.037054252 25.59837869 91 2.067336515 25.97891684 92 2.097439793 26.35720578 93 2.127355172 26.73313352 94 2.157073965 27.10659089 95 2.186587716 27.47747162 96 2.2158882 27.84567236 97 2.244967423 28.21109266 98 2.273817626 28.573635 99 2.302431282 28.9332048 100 2.330801099 29.28971043 101 2.358920018 29.64306319 102 2.386781214 29.99317731 103 2.414378094 30.33996993 104 2.441704298 30.68336114 105 2.468753694 31.02327388 106 2.49552038 31.35963397 107 2.52199868 31.6923701 108 2.548183141 32.02141374 109 2.574068533 32.34669917 110 2.599649846 32.66816343 111 2.624922283 32.98574624 112 2.649881263 33.29939003 113 2.674522412 33.60903984 114 2.698841562 33.9146433 115 2.722834749 34.21615057 116 2.746498203 34.51351431 117 2.769828351 34.8066896 118 2.792821809 35.09563391 119 2.815475375 35.38030702 120 2.837786031 35.66067099 121 2.859750932 35.93669008 122 2.881367405 36.20833069 123 2.902632943 36.47556132 124 2.923545198 36.73835247 125 2.944101981 36.99667662 126 2.964301252 37.25050814 127 2.984141115 37.49982322 128 3.003619819 37.74459982 129 3.022735743 37.98481762 130 3.041487401 38.2204579 131 3.059873429 38.45150354 132 3.077892583 38.67793891 133 3.095543736 38.89974984 134 3.112825868 39.11692352 135 3.129738065 39.32944845 136 3.146279512 39.5373144 137 3.162449488 39.74051231 138 3.178247363 39.93903426 139 3.19367259 40.13287338 140 3.208724703 40.32202382 141 3.223403312 40.50648066 142 3.237708097 40.68623989 143 3.251638803 40.86129831 144 3.265195239 41.03165351 145 3.27837727 41.19730379 146 3.291184815 41.35824814 147 3.30361784 41.51448615 148 3.31567636 41.66601798 149 3.327360427 41.81284429 150 3.338670133 41.95496625 151 3.349605603 42.09238542 152 3.360166992 42.22510375 153 3.370354482 42.35312352 154 3.380168278 42.47644732 155 3.389608605 42.59507796 156 3.398675705 42.7090185 157 3.407369835 42.81827216 158 3.415691262 42.9228423 159 3.423640263 43.02273239 160 3.431217119 43.11794598 161 3.438422116 43.20848663 162 3.445255539 43.29435797 163 3.451717675 43.37556356 164 3.457808804 43.45210695 165 3.463529204 43.52399161 166 3.468879142 43.59122091 167 3.473858878 43.65379813 168 3.478468663 43.71172639 169 3.482708732 43.76500867 170 3.486579309 43.81364777 171 3.490080602 43.85764631 172 3.493212802 43.8970067 173 3.495976084 43.93173114 174 3.498370606 43.96182158 175 3.500396502 43.98727974 176 3.502053892 44.00810712 177 3.503342872 44.02430491 178 3.504263517 44.03587408 179 3.504815882 44.04281531 180 3.505 44.045129 181 3.504815882 44.04281531 182 3.504263517 44.03587408 183 3.503342872 44.02430491 184 3.502053892 44.00810712 185 3.500396502 43.98727974 186 3.498370606 43.96182158 187 3.495976084 43.93173114 188 3.493212802 43.8970067 189 3.490080602 43.85764631 190 3.486579309 43.81364777 191 3.482708732 43.76500867 192 3.478468663 43.71172639 193 3.473858878 43.65379813 194 3.468879142 43.59122091 195 3.463529204 43.52399161 196 3.457808804 43.45210695 197 3.451717675 43.37556356 198 3.445255539 43.29435797 199 3.438422116 43.20848663 200 3.431217119 43.11794598 201 3.423640263 43.02273239 202 3.415691262 42.9228423 203 3.407369835 42.81827216 204 3.398675705 42.7090185 205 3.389608605 42.59507796 206 3.380168278 42.47644732 207 3.370354482 42.35312352 208 3.360166992 42.22510375 209 3.349605603 42.09238542 210 3.338670133 41.95496625 211 3.327360427 41.81284429 212 3.31567636 41.66601798 213 3.30361784 41.51448615 214 3.291184815 41.35824814 215 3.27837727 41.19730379 216 3.265195239 41.03165351 217 3.251638803 40.86129831 218 3.237708097 40.68623989 219 3.223403312 40.50648066 220 3.208724703 40.32202382 221 3.19367259 40.13287338 222 3.178247363 39.93903426 223 3.162449488 39.74051231 224 3.146279512 39.5373144 225 3.129738065 39.32944845 226 3.112825868 39.11692352 227 3.095543736 38.89974984 228 3.077892583 38.67793891 229 3.059873429 38.45150354 230 3.041487401 38.2204579 231 3.022735743 37.98481762 232 3.003619819 37.74459982 233 2.984141115 37.49982322 234 2.964301252 37.25050814 235 2.944101981 36.99667662 236 2.923545198 36.73835247 237 2.902632943 36.47556132 238 2.881367405 36.20833069 239 2.859750932 35.93669008 240 2.837786031 35.66067099 241 2.815475375 35.38030702 242 2.792821809 35.09563391 243 2.769828351 34.8066896 244 2.746498203 34.51351431 245 2.722834749 34.21615057 246 2.698841562 33.9146433 247 2.674522412 33.60903984 248 2.649881263 33.29939003 249 2.624922283 32.98574624 250 2.599649846 32.66816343 251 2.574068533 32.34669917 252 2.548183141 32.02141374 253 2.52199868 31.6923701 254 2.49552038 31.35963397 255 2.468753694 31.02327388 256 2.441704298 30.68336114 257 2.414378094 30.33996993 258 2.386781214 29.99317731 259 2.358920018 29.64306319 260 2.330801099 29.28971043 261 2.302431282 28.9332048 262 2.273817626 28.573635 263 2.244967423 28.21109266 264 2.2158882 27.84567236 265 2.186587716 27.47747162 266 2.157073965 27.10659089 267 2.127355172 26.73313352 268 2.097439793 26.35720578 269 2.067336515 25.97891684 270 2.037054252 25.59837869 271 2.006602141 25.21570618 272 1.975989545 24.83101695 273 1.945226044 24.4444314 274 1.914321436 24.05607264 275 1.883285731 23.66606647 276 1.852129148 23.2745413 277 1.820862108 22.88162809 278 1.789495235 22.48746033 279 1.758039343 22.09217394 280 1.72650544 21.69590723 281 1.694904714 21.29880079 282 1.66324853 20.90099745 283 1.631548425 20.50264218 284 1.599816101 20.10388205 285 1.568063417 19.70486605 286 1.536302382 19.30574511 287 1.504545147 18.90667193 288 1.472804 18.50780091 289 1.441091356 18.10928806 290 1.409419747 17.71129089 291 1.377801819 17.31396829 292 1.346250318 16.91748043 293 1.314778085 16.52198869 294 1.283398044 16.12765547 295 1.252123198 15.73464416 296 1.220966612 15.34311896 297 1.189941412 14.9532448 298 1.15906077 14.5651872 299 1.128337897 14.17911219 300 1.097786031 13.79518612 301 1.067418432 13.41357561 302 1.037248366 13.03444738 303 1.007289101 12.65796816 304 0.977553894 12.28430453 305 0.948055983 11.91362284 306 0.918808574 11.54608906 307 0.889824835 11.18186866 308 0.861117884 10.82112648 309 0.832700782 10.46402664 310 0.804586519 10.11073239 311 0.776788008 9.761405994 312 0.749318073 9.416208615 313 0.722189443 9.075300196 314 0.695414739 8.738839341 315 0.669006467 8.406983203 316 0.642977007 8.079887362 317 0.617338606 7.757705721 318 0.59210337 7.440590387 319 0.56728325 7.128691568 320 0.542890041 6.822157458 321 0.518935366 6.521134138 322 0.495430674 6.225765467 323 0.472387228 5.936192985 324 0.449816099 5.652555807 325 0.427728156 5.374990533 326 0.406134062 5.103631147 327 0.385044264 4.838608924 328 0.364468985 4.580052347 329 0.344418221 4.328087007 330 0.324901728 4.082835528 331 0.305929022 3.844417478 332 0.287509369 3.612949288 333 0.269651778 3.388544179 334 0.252364997 3.171312079 335 0.235657506 2.961359555 336 0.219537512 2.758789742 337 0.204012945 2.563702274 338 0.189091448 2.376193219 339 0.174780379 2.196355015 340 0.161086799 2.024276413 341 0.148017473 1.860042419 342 0.135578863 1.703734236 343 0.123777124 1.555429218 344 0.112618103 1.415200814 345 0.102107328 1.283118527 346 0.092250014 1.159247867 347 0.083051053 1.04365031 348 0.074515012 0.93638326 349 0.066646134 0.837500014 350 0.059448328 0.747049726 351 0.052925176 0.665077379 352 0.047079923 0.591623756 353 0.041915477 0.526725415 354 0.03743441 0.470414665 355 0.033638953 0.42271955 356 0.030530997 0.383663825 357 0.028112091 0.353266949 358 0.026383439 0.331544068 359 0.025345903 0.318506008
 

MolaKule

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Originally Posted by A_Harman
...Yes it is, but there is the complicating factor of compression ratio, which requires you to take into account the clearance volume at the top of the stroke, not just the swept volume. Now we're getting into semantics. When you say "cylinder", do you mean a simple geometric cylinder, or an engine cylinder, which includes clearance volume?...
As of now, we're basing the problem on a "simple geometric cylinder" with a total displacement volume of 262.3 inches^3 as given in the first post.
 
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Originally Posted by MolaKule
Originally Posted by A_Harman
...Yes it is, but there is the complicating factor of compression ratio, which requires you to take into account the clearance volume at the top of the stroke, not just the swept volume. Now we're getting into semantics. When you say "cylinder", do you mean a simple geometric cylinder, or an engine cylinder, which includes clearance volume?...
As of now, we're basing the problem on a "simple geometric cylinder" with a total displacement volume of 262.3 inches^3 as given in the first post.
So it would be 39.015 cubic inches.
 
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So if the total volume of any one cylinder is 1/6th of the total volume and that volume is at maximum at BDC and diminishes as you head to top dead center the 225 degrees I believe is halfway between zero and maximum volume. I am probably missing something with the connecting rod angle or something silly that I am not taking in account. I will let brighter minds prevail on this I suppose. 21.858 is my final grasp at this straw....
 
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I get a preliminary result of 40.73 in³, but didn't double-check my calculations yet. That assumes 4.000" bore, which is necessary to get the claimed displacement with 3.48" stroke. This does not include clearance volume.
 

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Thanks to all who participated in the Question of The Day and it was good to see the many number of responses. grin Those who gave an answer of 39.xx in.^3 or cubic inches deserve a big thumbsup Notice - I didn't ask about the Clearance Volume Vc or give the compression Ratio as that is for another QOTD and to keep this problem constrained within terms of the simpler Slider-Crank mechanical model. We know the maximum volume of each cylinder is 262.3 in.^3/6 = 43.72 in.^3 or cubic inches and this has to occur at 180 Degrees of crank angle or at Bottom Dead Center (BDC). At any other Crank Angle the Volume has to be less than 43.72 in.^3. We also know that maximum piston travel will be from Top Dead Center (TDC) to BDC or from BDC to TDC. What we need to know is: What is the piston position (x) for any given Crank Angle or x(Theta)? Once we know the piston position x we can multiply that by the Bore area BA, since Area times Length = Volume. Data Given ("*" means Multiplication): B = 4.012; Total Diameter of Bore in inches S = 3.48; Stroke in inches VD = 262.3; Total Cubic inches of Displacement N = 6; Number of cylinders L = 5.7; Length of connecting in inches from bore to bore 225 Degrees Crank Rotation. Determine Total Displacement per cylinder Vp = VD/N = 43.72 in.^3; Determine Bore Area; BA = pi/4*(B^2) = 12.6419 in.^2 or square Inches; Determine Crank Radius from Stroke: a = S/2 = 1.74 inches; Crank Radius; Convert Degrees to Radians: ThetaDeg = 225; ThetaRad = ThetaDeg/57.3 = 3.9267 Radians; Determine Position of Piston verses Crank Angle from Geometry of Problem : x = a + L - [SQRT(L^2 - a^2*sin(ThetaRad)^2] - a*cos(ThetaRad) = 3.11 inches; Since V is a function of x as in V(x), determine Volume for x position at 225 degrees of Crank Angle. V = x*BA = 39.2533 or 39.3 cubic inches or in.^3 is the cylinder Volume at 225 degrees of Crank Angle which means the piston is on its up stroke travelling towards TDC. The volume would be the same at 135 degrees of crank angle but the piston would be on its down stroke towards BDC.
 
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