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

${\textrm {C}}_{2}{\textrm {H}}_{6}{\textrm {O}}+3{\textrm {O}}_{2}\to 2{\textrm {CO}}_{2}+3{\textrm {H}}_{2}{\textrm {O}}$

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.

Maximum Flying Distance

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

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

The distance covered by a projectile with initial velocity $v_0$ 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 s = \frac{v_0^2}{g}\sin(2\alpha) = \frac{}{}}

The drag coefficient 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_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