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