Ethanol Rocket

Theory

Ethanol 3d model

• 

  The Ethanol

• 

  C2H6O

• 

  The Ethanol

Atom positions

-1.1712	0.2997	0.0000	O
-0.0463	-0.5665	0.0000	C
1.2175	0.2668	0.0000	C
-0.0958	-1.2120	0.8819	H
-0.0952	-1.1938	-0.8946	H
2.1050	-0.3720	-0.0177	H
1.2426	0.9307	-0.8704	H
1.2616	0.9052	0.8886	H
-1.1291	0.8364	0.8099	H

HCH bonds are assumed to be undistorded tetraherdal angle 109.5 degrees. Actually the electrons repeal each other. The HOC bond is 104.5 deg because. . .

Valence shell electron-pair repulsion theory (VSEPR theory). . .

Van der Waals radius

Atom	Radius	Relative radius
C	170 pm	1.42
H	120 pm	1.00
O	152 pm	1.27

Use CPK coloring convention, white (hydrogen), black (carbon) and red (oxygen).

Ethanol reaction with Oxygen and Air

Ethanol reaction with oxygen

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \textrm{C}_2 \textrm H_6 \textrm O + 3\textrm O_2 \to 2 \textrm{CO}_2 + 3 \textrm H_2\textrm O }

The molecular weight of ethanol is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 46.069} g/mol, and the molar weight of oxygen is 32 g/mol. The oxygen--ethanol fuel ratio is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3\times 32 / 46 = 2.1} . We need Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2.1 } kg of oxygen to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1} kg of ethanol. The air consists of 23.2 mass-% of oxygen, thus the air--ethanol ratio is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2.1/0.232 = 9} .

The volume-% of oxygen in air is 20.9%. The volume of the bottle is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V = 500 } ml which gives the amount of oxygen to be Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0.209 V = 0.209 \times 500 = 104.5} ml Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle =0.1045\times1.314 = 0.137 } g of oxygen, which gives the amount of ethanol Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0.137 / 2.1 = 0.0659 } g Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle =0.0659/0.789= 0.0834} ml. OR directly using air--ethanol ratio we have Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho V/9 = 1.2041 \times 0.5 /9 = 0.066} gram. That amount equals to Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V/\rho_\textrm{Ethanol} = 0.066g/(789g/l) = 0.084 } ml Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle =84 } mm³. Almost the same result using the methods. See the attached spreadsheet for detailed calculations.

The energy released by burning ethanol is 17.9 kJ/ml. Thus, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0.084} ml of ethanol releases Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1,50} kJ of energy. This energy is converted into heat, sound and projectile motion (plus others).

Densities

	Density Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rho}	At
Oxygen (g)	1.429 g/l	STP
Oxygen (g)	1.314 g/l	20 °C
Ethanol (l)	789.45 g/l	20 °C
Air (l)	1.2041 g/l	20 °C

File:Ethanol oxygen combustion.ods

The inner diameter of the rocket bottle is 25 mm. The height of the ethanol in the cap need to be Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V = \pi r^2 h \iff h = \frac{V}{\pi r^2} = \frac{84 mm^3 }{ \pi 12.5^2 mm^2} = 0.17 } mm.

Exothermic Reaction and Energy release

Specific Heat

The energy is transferred into pressure, sound, etc. The isochoric specific heat Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_v</math of air is <math>C_v = 0.7171} kJ/(kgK) at 18 centigrade. At 180 degrees Celsius Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_v = 0.7352} kJ/(kgK). Thus, the energy released heats

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{align} \Delta E &= C_v \Delta T m \\ \Delta T &= \frac{\Delta E}{C_v m} &=\frac{1.5 kJ}{0.7 kJ/(kgK) \times 0.5 \times 10^{-3}} \\ &= 2100 K \end{align} }

Ideal gas law

The simplest idea is to use ideal gas law Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle pV = nRT } gives Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p} which gives force $F=pA$ where </math>A</math> is the diameter of the nozzle.

Detonation velocity

Burn rate, detonation velocity. https://en.wikipedia.org/wiki/Table_of_explosive_detonation_velocities

http://www.explosionsolutions.co.uk/110411016.pdf

https://link.springer.com/article/10.1007/s00193-015-0554-7 $v=1500$ m/s???

Horizontal(?) accelaration due to rapidly expanding air.

Benjamin Robins:

$F(x)={\frac {RPAc}{x}}$

where $x$ distance in barrel, $R$ is the initial ratio of hot gas pressure to atmospheric pressure, $P$ is the atmospheric pressure, $A$ is the cross-sectional area of the ball or bore, $c$ is the length of the barrel occupied by the powder charge before ignition.

$E_{k}=\int _{0}^{L}F(x)dx\iff v_{0}^{2}={\frac {2RP}{m}}{\frac {\pi d^{2}c}{4}}\ln(L/c)$

where $d$ is the barrel diameter (the bore)

The powder change $p$ is given by $p={\frac {\pi d^{2}c}{4}}\eta$ where $\eta$ is the density of gunpowder.

--

https://www.arc.id.au/RobinsOnBallistics.html

The pressure falls as $1/x$.

--

Bernoulli?

--

$\sum F=0$

$F=ma=pA\iff F=m{\frac {d^{2}x}{dt^{2}}}$

$F=m{\frac {dv}{dt}}=mv{\frac {dv}{dx}}=pA\iff mvdv=pAdx$

$\int mvdv=\int _{0}^{L}pAdx$

where

${\frac {1}{L}}\int _{0}^{L}Pdx=averagepressure={\vec {p}}$

If $A$ is constant

Failed to parse (syntax error): {\displaystyle \frac12 mv^2 = A \int_0^L p dx = A \vec p L }

then

$v={\sqrt {\frac {2{\vec {p}}AL}{mc_{f}}}}$ and ${\vec {p}}={\frac {c_{f}mv^{2}}{2AL}}$

Projectile friction, rotational energy, heat transfer: correction factor Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_f} .

The average pressure is 25% of peak pressure

--

http://closefocusresearch.com/calculating-barrel-pressure-and-projectile-velocity-gun-systems

https://www.arc.id.au/CannonBallistics.html

Maximum Flying Distance

By the conservation of energy, all explosive energy is transferred into the kinetic energy.

$E_{\textrm {explosion}}=E_{\text{kinetic}}$

The distance covered by a projectile with initial velocity $v_0$ is

$s={\frac {v_{0}^{2}}{g}}\sin(2\alpha )={\frac {}{}}$

The drag coefficient $c_{d}$ needs to be found. For the circular disc (a coin) the drag coefficient is almost constant for all velocities (Reynold numbers). The coefficient of drag for a cylinder in this orientation is about 0.81 so long as the length to diameter ratio is greater than 2, see http://www.aerospaceweb.org/question/aerodynamics/q0231.shtml. The cone in either end gives some complications.

The drag equation for the drag force is Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle F_D = \frac12 \rho v^2 c_d A} .

Piezo Crystal

To ignite the air--ethanol mixture, we use piezo crystal. When tjhe piezo crystal is compressed, it will generate an electric charge which creates a spark.

References

https://nptel.ac.in/content/storage2/courses/123106002/MODULE%20-%20I/Lecture%201.pdf

https://www.peacesoftware.de/einigewerte/o2_e.html

http://www.users.miamioh.edu/sommerad/NSF%20Files/drag_coefficient_calculation.pdf

DRAG COEFFICIENTS FOR FLAT PLATES , SPHERES, AND CYLINDERS MOVING AT LOW REYNOLDS NUMBERS IN A VISCOUS FLUID by ALVA MERLE JONES

http://www.aerospaceweb.org/question/aerodynamics/q0231.shtml

Ethanol rockets

https://www.youtube.com/watch?v=zTwz6FGobCA Ethanol Rocket - Cool Science Experiment

https://www.youtube.com/watch?v=4s-SZypWxeg Ethanol Explosion - Cool Science Experiment