# Physic Behind Sky Lanterns

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## Introduction: Physic Behind Sky Lanterns

Hello everyone,

in this instructable I will explain the principle of flight hot air balloon (known as sky lanterns). I had hot air balloons for school project, so,I thought that it might be interested to other people see how hot air balloons works and I translate it from my language.
About tutorial for making hot air balloons, there is full instructable.com of it,so, just search a little bit. :)

Sorry for possible grammar mistakes in advice, english isn't my mother language.

If you have any questions, or ideas for some new projects, just ask below or send me PM.

So, here we go! :D

If you will like it, feel free to vote!

## Step 1: Historical Introduction

What are hot air balloons?

As you may already figured it out, hot air balloon in basic is just some big bag in which you put heated air,which is produced by some fire source, so it could fly.

• Hot air balloons were used in WW2 by Japan, they were bombing America, principle was that they were catching air streams for navigation, and then when they will get to target place, they will just shut down the flame. It is surprising that sometimes they would hit something, but they stopped because they did not know whether it working or not.
• About sky lanterns, they were usually made from rice paper and bamboo frame, whole balloon was powered by bamboo paper dipped in wax. The principle is that fire heat up the air in the balloon which creates lift, and then lift is greater than balloon weight then it starts to rise. First great hot air balloon, was made by brothers Etienne & Joseph Montolfier. The balloon was made from paper and powered with burning thatch, volume of 800 m^3. It reached high of 2000 m and landed couple kilometers away.
• Today, hot air balloons are used in sports, sky lanterns are used for some special occasions like birthday parties, new year celebrations, etc.

## Step 2: The Idea of Work:

• Through a series of experiments and measurements I intend to determine the optimal design of the balloon (balloon volume, the necessary power and combustion of fuel, the weight of the entire structure)

• I want to examine how does temperature changes in the balloon with in time depending on: different power sources speed of balloon and acceleration.

The main questions are:

1. Which fuel is the best to propel the balloon?
2. Is it better to use a larger or smaller balloon?

Hypothesis is:

1. Hydrogen, because it is lightweight and has no carbon which could make whole gas heavier.

2. Bigger, because the surface of balloon rises on a square, and volume on third, so that the ratio of the air stored in the smaller and larger balloon is different.

And now lets prove that!

## Step 3: Sketch 1: Motion of Air Inside the Balloon

Theory:

• Lanterns fly on the principle of lift in the air. By heating the air in the lantern, air get warmer from the environment, which is why it has a lower density, it creates a lift which, when it becomes greater than the weight lanterns, lantern lifted into the air.

Sketch 1 shows air motion inside the balloon, I think that all is pretty good shown. :)

## Step 4: Hydrostatic Pressure

Pressure (p) is defined as the ratio of the force (F) and the surface (A) to which the force acts at right angles. We can write the formula: p=F/A

Excerpt hydrostatic pressure:

p_hs=F/A =(m∙g)/A=(ρ∙V∙g)/A=(ρ∙h∙A∙g)/A=ρ∙g∙h

p_hs=ρ∙g∙h

At a depth (h) imagine a plane parallel to the surface (A) of the liquid. On the surface of a liquid weight acting cylinder height h. First, determine how much of the volume V have the cylinder:

V = A h

The mass of the cylinder fluid can be expressed from the density ( ρ = m/v )

m = V ρ so it is: m = A h ρ

and the weight of the cylinder (G = m g) is:

G = A h ρ g

Since pressure is equal to the ratio of the weight of fluid and the surface upon which it operates, the expression for the hydrostatic pressure follows:

p = ρ g h

## Step 5: Buoyancy:

• Buoyancy is the force that acts on all bodies steeped in fluids (liquids and gases) that are found in the potential field force (gravitational field, accelerated system), and it is happening because of difference which is made due to the hydrostatic pressure acting on the upper and lower part.

Since in our case we have the density of the air out of the balloon and the density of gas in the balloon, we need in our calculation:

F_u=∆ρ∙g∙V

where: ∆ρ=ρ_z - ρ_b => is the difference density of gas inside and outside the balloon

The general state equation of gas:

p∙V=n∙R∙T

p∙V=m/M_r ∙R∙T

p∙M_r=m/V∙R∙T

p∙Mr=ρ∙R∙T

Those equations allows us to calculate density of gas, which follows:

ρ=(p∙M_r)/(R∙T)

The molar mass of air:

• Air is a mixture of different gases from which the most common is nitrogen (78%), oxygen (21%) and argon (1%). This is why its molar mass is:

M_r (air)=0.78∙M_r (N_2 )+0.21∙M_r (O_2 )+0.01∙M_r (Ar)

M_r (air)=0.78(2∙14)+0,21∙(2∙16)+0,01∙(40)

M_r (air)=29g/mol

In the text we have used the following physical values and constants:

F1- force from up_ _____________ g- gravitational constant

F2 - force from down____________ρ- density

F3,F4- side forces ______________Fu- lift force

p-preasure ____________________p_a- atmospheric pressure

F - force ______________________n- number of moles

A, S- surface area_______________R- general gas constant

p_hs- hydrostatic pressure_______ M_r- the molar mass of gas

m- weight-_ ___________________ T - temperature in kelvins

V- volume_____________________p_b- density of air inside the balloon

∆p- pressure difference inside and outside the balloon

p_z- air density outside the balloon

Fuel:

• As fuel I have used paraffin candles. They consist of a solid fuel and sort of fuse usually made from cotton fabric which are surrounded by paraffin which melts at a low temperature (typically about 60 ° C).

• Capillary action of the wick wax is transferred to a flame where it vaporizes and burns in the presence of oxygen. The candle is extinguished when the oxygen content in the air falls below about 16%.

Choosing a fuel:

• It would be great if I as a source of heat was able to torch hydrogen in oxygen, because burning hydrogen produces only water vapor (no carbon dioxide), which is a good choice for lifting the balloon due to its low molecular weight (M_r (H20) = 18g/mol ). Hydrogen, however, could not be used for safety reasons.

• When burning candle (paraffin) it releases a certain ratio of CO2 and H2O. As there more water vapor in the mixture of air in the balloon lighter. CO2 is not desirable in a balloon because it makes the air more massive , since it is the molar weight of greater than air (M_r (CO2) = 44g/mol).

• A mixture of paraffin hydrocarbons with chain length of 20 carbon atoms. Such molecules have approximately 2H atoms on a single atom C and by combustion they give approximately the same number of molecules of CO2 and H20. Later, in some of the measurements, as a heat source is used hot air blower. Thus I get the safety, speed and simplicity in performing measurements.

Calculation of the molar mass of gas in the balloon when using candle:

Cold air from the outside comes to the point of burning and there is oxygen from it combines with hydrogen and carbon from paraffin. Nitrogen enters the balloon unchanged.

100 molecules of air (approximately 79% N2 and 21% O2) that entered into the balloon created 107 molecules (79 molecules of N2, 14 and 14 molecules of CO2 molecules H20) and from that we get equation:

M_r (balloon)=1/1.07(0.79∙M_r (N_2 )+0.14∙M_r (CO_2 )+0.14∙M_r (H_2 O)

M_r(mixture in the balloon)=28,8g/mol

The experiment:

Materials:

The material for the balloon I chose to be lightweight, tight enough and easily procurable. I took a plastic trash bags volume of 35 liters. Frame structure and carrier candles are made of balsa planks (wood of very low density ). As fuel I used different compounds and mixtures (liquid and solid), but in the end I decided to use an ordinary small birthday candles because they were the easiest to handle.

Characteristics of candles:

The mass of candle: 1 gram
Height of candle: 5.4 cm

Burning rate: 0.0010 g / s

Heat value of paraffin: 46 MJ / kg

Heating power one candle: 46 W

## Step 6: Measurements:

Images show schematic principle of measuring, description are in images.

Digital multimeter is Vernier LabQuest.

Measuring buoyancy of balloon:

On the balloon I put the weight that it could not fly and so I could perform accurate measurements. Candles were placed on the table for more precise measurements.

Temperature measurement in the balloon:

On the balloon was hanged weight to balloon would fly away. The probe was placed over a flame in the middle of the balloon.

Measuring the position, velocity and acceleration of of balloons:

For balloon I tied only five candles and put them under the speed measuring device. I measured the motion of balloon in the first 1.3 meters of raising. The device measured the positions of balloon in time, and the speed and acceleration I calculate using the software are provided with the device (logger pro) .

Device for speed measuring:

The device consists of an ultrasonic transmitter (sensor) connected to a measuring device Vernier LabQuest. The sensor works by transmitting ultrasonic signals within a relatively narrow beam of at the subject which measures the position. The signals are reflected by the target object, and return back to the sensor. The measuring device from the elapsed time calculate distance to the object, and from this the later can easily calculate the speed and acceleration of the object observed.

## Step 7: The Results of Measurements With a Balloon of 40 Liters:

Graph shows the grown lift force in time from start of heating of balloon. In the first 50 seconds, the lift force increases as the inside of of balloon is heated. When the temperature in a balloon stabilizes (heating = cooling through the walls of of balloons) force stops growing and remains constant.

## Step 8: Lift of Balloon, Depending on the Temperature

It can be seen that the measured values of lift is less than theoretical. That explained as a consequence of the method of measuring the temperature in a balloon. The temperature probe was placed in the middle of the upper part of of balloons where the temperature is higher than average. In the lower parts of the walls of the of balloon and the temperature is lower than the measured and lift is smaller.

Theoretical calculation of lift i calculated like that:

F_u=gV_b (ρ_z-ρ_b )

Where are ρ_z density of air outside, and ρ_b density of gas inside of balloon:

ρ_b=(p_z Mr_b)/RT

## Step 9: Temperature in Balloon

The temperature in a balloon, as expected, has grown with the number of candles that warmed the air. In second graph, we see that in the beginning of the temperature in a balloon grows rapidly, and as it approaches the maximum, thus grow more slowly (due to the simultaneous cooling in the space).

## Step 11: The Results of Measurements With a Balloon of 270 Liters.

Smaller balloons have developed quite a little lift (up to 0.07 N) so the measurement of such a small force was problematic. Digital dynamometer has a resolution of 0,001 N, but the last digit in the the reading is not certain. So I decided to make a new series of measurements with a larger balloon volume of about 270 liters.

For this balloon I did not use candles as a source of ignition because they need us a lot, and they don't burn at same rate every rate. I used a device that blows out hot air. It works on the same principle as hair dryer, but it only develops air temperature up to 500 ° C and blown up to 480 liters per minute. With these modifications, I achieved a buoyancy greater than 1 N which has significantly improved the quality of the measurement. This time, I measured the force during the warming-up of balloon, but first I warmed up balloon to a temperature of about 100 ° C, then I turn of the heating, turn on measuring the of force and let the balloon cools.

## Step 12: Measurements:

And, just to say, ignore negative values, that is because of sensor position, sometimes the balloon was going from the sensor, sometimes to the sensor.

Combining first two graphs, we show the dependence of lift on the balloon on the temperature inside the vessel. Measured data can be compared with the theoretical predicted:

F_u=gV_b (ρ_z-ρ_b )

On the graph we see a solid agreement of the measured data with the theoretical to some 90 ° C. After that experimental data begin vary significantly of predicted values. Possible reasons for this behavior are as follows:
At high temperatures, the volume of of balloons rises above the "normal" size, because it more blows. It is possible that at the time of the measurements there is a flow of air from the balloon outward which can act as an additional reactive propulsion. It should carry out additional measurements with constant heat source that would allow the temperature in a balloon maintains constant at will for a long time and it is changing the heating power can be adjusted as desired.

## Step 13: Measuring the Acceleration:

Balloon volume of 270 liters I warmed up with gun for hot air to a temperature of 100 ° C and then I let him it lifted up to the speed sensor which I mounted on the ceiling of the classroom.

## Step 14: Measurements 2#

We see that the data can be a great gird to parabola, which means that the motion of of balloons almost equally accelerated. From the graph we're picking the acceleration motion of balloons:

a=0,701 m/s2 (Acceleration is a double coefficient with x ^ 2)

The black line (in speed graph) shows the arithmetical average and it is obvious that the balloon moves equally accelerated. Comparison with the line is very good. Coefficient of the x has the meaning of acceleration of balloon, and balloon acceleration is according to the graph:
a = 0.696 m/s2 as expected, the same value as in the s-t graph

The black line( in acceleration graph) shows the trend of acceleration. These are the results of measuring up to 1.2 m in height so that air resistance does not have a greater impact on acceleration, but can be seen that acceleration is still slowly decreasing as we expected, in order to resist the air, which increases with speed.

## Step 15: DISCUSSION:

Data and measurements that I got were quite similar to my expectations .

I assumed that the balloon has a specific acceleration time when rising. As the speed increases, and therefore the air resistance , acceleration of the balloon decreases . Initially I assumed that the different composition of the gas inside and outside the balloon should affect buoyancy , but it turned out that the molar mass of air and gas in the balloon about the same , so the composition of the gas in the balloon has no significant impact . Noticeable impact would be given only if we use hydrogen as a fuel or a light hydrocarbon ( e.g. methane ) . Since we have measurements for later use with a larger balloon blower hot air in the balloon , we only had air that had no different chemical properties than the outside air . The difference in the theoretical and experimental data on the buoyancy caused by the method of measuring the temperature in the balloon . The mean temperature is certainly smaller than ours because the edge comes to cooling , and our probe was located in the middle of the balloon at the top where it is already hot ascending flow .

About aerodynamics, the best shape would be like drop of water, it's because the water when falling through the air form the best aerodynamic shape.

-So, we proved our hypothesis which I mention on beginning,

And, for the end of presentation, here is video which I recorded with camera mounted on big hot air balloon. The quality of video isn't something special (camera from ebay for \$10), balloon had about 1800 liter, mass of camera was 50g :

and some more:

Third Prize in the
Scientific Method Contest

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## Questions

I'm doing a project for the science fair on floating lanterns, so all of this information is very useful! Thank You!

This is very good but has one error. The Japanese vengeance balloons of WW2 used hydrogen as the lifting gas.

THX a lot

This is really educating even I dont know much physics

Great work Ivver!

I'm realy glad ( and proud ) to see you here...

Thank you! :)

awesome with the explanation

thank you! :-)

hehe cool

Thank you for your support, I'm very glad that you liked it. You can freely PM me if you are having trouble with something, I'll see if I can help. You have some nice instructables, I'll vote for you.

Admittedly I only skimmed over this but I didnt see anything about delta t. It certainly seems that the data would change significantly depending on the temperature of the room (outside air). ie if the room temperature is 22.2 degrees Celsius and the air in the balloon is heated to 100C the delta t is 77.8 degrees. But what if we have an outside air temp of 32.2 degrees Celsius, do we then have to heat the inside air to 110C in order to achieve the same result? In this line of thought, would it be more relevant to have recorded the delta t instead of the internal temperature of the balloon, since the internal temp seems irrelevant...

I didn't do that measurements because I could not control room temperature in that scale, but, I can give you the answer. You can calculate it with formula for lift: F_u=gV_b (ρ_z-ρ_b ) , where "g" is grav. constant, V_b is volume of balloon, p_z is density of air which is in room and p_b is density of air in balloon. About density of gases on different temperatures, you can use this calculator if you don't like paper job: http://yeroc.us/calculators/gas-density.php (air has 29g/mol)

We have to heat up air inside of balloon more than delta t to have same results as the one with lower room temperature.

You might have problems with your grammar but your physics rocks :)