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- THE MATHEMATICS OF SOMA BODY MECHANICS
- The formula for KE is;
- KE = Velocity * Velocity = n1, n1 * Mass = n2, n2 * 0.5 = n3 = KE
- or;
- KE = V * V = n1, n1 * M = n2, n2 * 0.5 = n3 = KE
- An object's structual strength can be expressed in two ways; tensile and compressive strength, both of which are measured in pascals/m2. Tensile strength is used when the object is pulled, swung or struck on it's sides. Compressive strength is used when the object is loaded with a weight on it's top, or pushed from it's bottom.
- The surface area of an object has to be determined before we can determine it's strength in pascals. Since the circle is the best model of the shapes found in living beings, it's formula will be the first presented;
- Area = Radius * Radius = n1, n1 * pi(3.14) = n2 = Area
- To calculate strength in pascals;
- Area(m2) / 1(m2) = n1, n1 * Pascals = n2 = nPa
- If KE exceeds nPa, the object is broken. If nPa exceeds KE, the object resists destruction;
- Destruction = KE = n+, nPa = n- = Destuction
- Survival = nPa = n+, KE = n- = Survival
- This applies to both tensile and compressive strengths, but note the difference in definition, and note also that natural materials often differ in their tensile and compressive strengths.
- The Soma body can be divided into certain key points where knowing the tensile and compressive strengths is important, most notably;
- - Wrist (Weakest link in the arm)
- - Ankle (Weakest link in the leg)
- - Chest
- Any stress that could be put on the rest of the body either transfers through these locations, or survives at least the KE the wrist or ankle is rated for by virtue of exceeding their areas in cross section.
- Our model Soma body will be the Somamba, or 'Mother of All Soma;'
- To find area;
- Area = pi(3.14) * 2 = n1, C / n1 = R = n2, n2 * n2 = n3, pi(3.14) * n3 = n4 = Area
- Where C is circumference and R is Radius.
- Somamba's calculated values are;
- Head A1, Eye A2, Hair A3
- Neck B1
- Chest C1
- Abdomen D1
- Upper arm E1, Lower arm E2, Hand E3
- Thigh F1, Calf F2, Ankle F3, Foot F4
- Height G1
- Weight H1
- A1-0.5575m, 22", 0.0247332m2, Tensile 3,215,316,000N, Compressive 618,330,000N
- A2-0.0254m, 1", 5.13402E-5m2, Tensile 6,674,226N, Compressive 1,283,505N
- A3-1.7E-5m, 0.00066929", 2.29979E-11m2, Tensile 2.989727N, Compressive 0.5749475N
- B1-0.305m, 12.00785", 0.00740269m2, Tensile 962,349,700N, Compressive 185,067,250N
- C1-0.6096m, 23.999952", 0.029572m2, Tensile 3,844,360,000N, Compressive 739,300,000N
- D1-0.434m, 17.08658", 0.0149889m2, Tensile 1,948,557,000N, Compressive 374,722,500N
- E1-0.342m, 13.46454", 0.0093077m2, Tensile 1,210,001,000N, Compressive 232,692,500N
- E2-0.09906m, 3.8999922", 0.000780884m2, Tensile 101,514,920N, Compressive 19,522,100N
- E3-0.023706666666666657m, 0.933331466666666", 4.4723E-5m2, Tensile 5,813,990N, Compressive 1,118,075N
- F1-0.588m, 23.14956", 0.0275134m2, Tensile 3,576,742,000N, Compressive 687,835,000N
- F2-0.329m, 12.95273", 0.00861355m2, Tensile 1,119,761,500N, Compressive 215,338,750N
- F3-0.09906m, 3.8999922", 0.000780884m2, Tensile 101,514,920N, Compressive 19,522,100N
- F4-0.0254m, 0.999998", 5.13402E-5m2, Tensile 6,674,226N, Compressive 1,283,505N
- G1-1.422m
- H1-7.1344kg(49kg)
- Obviously, the compressive strength is the absolute limit for any limb. Using two limbs doubles the force in Newtons which can be survived.
- Aerographene can compress by 90% - meaning that a 1m3 object could reduce it's volume to 0.1m3. Aerographene weighs 0.16mg/cm3, meaning a 1m3 object would weigh 160g. Aerographene can hold 900 times it's own weight in oil, meaning that 160g of AG could hold 144kg of gasoline - which holds 37.4MJ/L, meaning that this object could hold 37,400MJ.
- Somamba has a body volume of 49,000cm3;
- 490,000cm3 AG @ 90% Compression * 0.16mg/cm3 = 78,400mg = 78.4g/49,000cm3
- 37.4MJ/L * 49,000 / 1,000 = 1,832.6MJ/49L/7.056kg
- 78.4g + 7.056kg = 7.1344kg
- 1N moves 1kg 1m;
- 1N/1kg/1m
- KE = V * V = n1, n1 * M = n2, n2 * 0.5 = n3 = KE
- KE(559.8500724396445) = 559.8500724396445m/s * 559.8500724396445m/s = 313,432.103610675 (n1), n1 * 7.1344kg = 2,236,150 (n2), n2 * 0.5 = 1,118,075 (n3) = KE(559.8500724396445)
- KE(559.8500724396445) = Max Survivable Velocity
- The foot limits the maximum lift, and two feet doubles it;
- 1,118,075kg(1.118075Mt) * 2 = 2,236,150kg(2.23615Mt)
- Muscles can be 95% efficient, so;
- 100% effciency * 95% = 1.052631578947368(n1), n1 = KE(2,367)NeN(1.05), MtNeN(1.05)
- KE(559.8500724396445) * (1.05) = 1,176,921.052631578N, 1.118075MtNeN * (1.05) = 1,176,921.052631578N, 2.23615MtNeN * (1.05) = 2,353,842.105263157N
- Power;
- Volume of a cylinder;
- Vol = R * R = n1, pi(3.14) * n1 = n2, n2 * H = Vol,
- 0.000013571680264m3 = 0.06 * 0.06 = 0.0036, pi(3.14) * 0.0036 = 0.011309733552923, 0.011309733552923 * 0.0012 = 0.000013571680264m3
- Surface area of the cylinder;
- Surface area = R * R = n1, pi(3.14) * n1 = n2 = Surface area,
- 0.011309733552923m = 0.06 * 0.06 = 0.0036, pi(3.14) * 0.0036 = 0.011309733552923m
- To calculate Rotational energy;
- Angular momentum = Radius * Radius = n1, n1 * Mass = n2 = Angular momentum,
- Angular velocity = pi(3.14) * 2 = n1, n1 / 0.0175 * RPM = Angular velocity,
- Moment of inertia = Angular momentum / Angular velocity = n1 = Moment of inertia,
- Rotational Energy = AV * AV = n1, MOI * n1 = n2, n2 * 2 = n3 = Rotational Energy
- One disk = 0.00217g, Radius 0.06m, Thickness 0.0012m, TensilePa 1,470,261,000, RPM 1,400,000,000, Rotational Energy 7,853,478.979149691N
- 50 Disks = 0.1085g, Radius 0.06m, Thickness 0.06m, Rotational Energy 392,673,948.95748N
- 392,673,948.95748 / 1,176,921.052631578 = 333.6451056589283 Max V's
- 392,673,948.95748 / 1,176,921.052631578 = 333.6451056589283 One-hand lift
- 392,673,948.95748 / 2,353,842.105263157 = 166.8225528294641 Two-hand lift
- Calculating parabolic arcs;
- To calculate the vertical(Vy) and horizontal(Vx) velocities;
- angle(cos) = n1, V * n1 = n2 = Vx
- angle(sin) = n1, V * n1 = n2 = Vy
- To calculate time(Ty) spent reaching Max height(Dy);
- Ty = 0 - Vy = n1, n1 * -G = n2 = Ty
- To calculate Max height(Dy);
- Dy = Vy * Ty = n1, 0.5 * -G = n2, n2 * Ty = n3, n2 * n3 = n4 = Dy
- To calculate time spent in the air(Ty2);
- Ty * 2 = Ty2
- To calculate range(Dx);
- Dx = Vy * Ty2 = n1 = Dx
- Graphene-Laser-Electron Propulsion(GLEPnir);
- >http://arxiv.org/pdf/1505.04254.pdf
- >pp13
- >Figure d, Kinetic energy distribution spectrum of electrons emitted from graphene sponge under laser (450 nm) illumination showed a broad energy distribution
- >4.25E4 mW cm-2
- 42,500mW = 42.5W, cm-2 = 0.01cm, so 42.5W/0.01cm. 1cm / 0.01cm = 100(1)cm, 42.5 * 100 = 4,250W of thrust per square centimeter.
- 1W = 1N, so one single square centmeter of graphene can produce 4,250N of thrust. 1N lifts 1kg.
- 1eV = 1.60217656535 x 10-19N
- 1g of Carbon = 1.3351667e+23 = nElectron
- eV = neV * 1.60217656535 x 10-19N
- 75 * 1.60217656535 x 10e-19N = 1.2016324e-16N
- 1.2016324e-16N * nElectron(1.3351667e+23) = 16,043,795.6512N
- cm-2 = 0.1mm = n1, n1 * n1 = 0.01mm2
- Cube root of 16,043,795.6512 = 252.2139132846656
- 252.2139132846656 * 252.2139132846656 = 63,611.85805436484N/0.01mm2
- 63,611.85805436484N/0.01mm2
- 84W Laser = 42.5N = 50.5952380952381% Conversion Efficiency
- 63,611.85805436484N/0.01mm2 @ 125,726.9665074505N
- BSA = Mass * 0.425 = n1, n1 * 0.007184 = n2, Height * 0.725 = n3, n2 * n3 = n4, n4 * 0.1 = n5 = BSA
- Calculating Somamba's BSA;
- BSA = (114lbs) * 0.425 = 48.45, 48.45 * 0.007184 = 0.3480648, 56" * 0.725 = 40.6, 0.3480648 * 40.6 = 14.13143088, 14.13143088 * 0.1 = 1.413143088 = BSA
- 1m2 = 10,000cm2,
- 1.413143088m2 = 14,131.43088cm2,
- 14,131.43088cm2 * 4,250N = 60,058,581.24N,
- KE = V * V = n1, n1 * M = n2, n2 * 0.5 = n3 = KE
- KE = 4,103.210568588052 * 4,103.210568588052 = 16,836,336.97017268, 16,836,336.97017268 * 7.1344kg = 120,117,162.48, 120,117,162.48 * 0.5 = 60,058,581.24N = KE
- Somamba BSA = 1.413143088m2 = 1,413,143.088mm2 / 0.01 = 141,314,308.8mm2
- 141,314,308.8mm2 * 63,611.85805436484N = 8,989,265,800,000N @ 4.5481404345238e+12N
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