Electrostatic lighter

Ancient people used to make fire by rubbing wood. Propose an alternative setup, based on electrostatic effects, made from materials available to Bronze Age people. Make a device capable of setting fire using just static electricity in the shortest time possible to a piece of wood.

Introduction

Literature Review

The link between static electricity and fire

How do electrostatic generators work ?

Testing a Wimshurst machine

Setting the fire

What did our work produce ?

Who are we ?

Bibliography

INTRODUCTION

To answer the problem, the main focus points will be the following questions :

How to be able to set fire to a piece of wood ?

In the shortest time possible ?

Using electrostatic effects ?

With a device built of materials available at the Bronze Age (3,300 BCE to 1,200 BCE) ?

LITERATURE REVIEW

The links between static electricity and fire

"In July 2002, during the shutdown of a certain aniline plant, compressed air was used to add catalyst to the fluidized bed. The electrostatic spark detonated the hydrogen released by the residual unregenerated catalyst in the system, causing the explosion-proof membrane to rupture.
On December 26, 2002, a petrochemical company's tank truck recovered dirty oil. The tank truck's electrostatic grounding facilities were incomplete, and the pump outlet used a fire hose with poor conductivity, causing static electricity to accumulate and causing the tank truck to explode."

Source : https://www.staticgrounding.cn/

There are numerous reports of industrial fires caused by a spark in a confined environment containing volatile materials.
Therefrom, our strategy will be to create a spark in such an environment. To achieve that we will need an electrostatic generator.

How do electrostatic generators work ?

*Van de Graaff generator*
Picture source : wikipedia

Friction machines

An insulator is moving between the two electrodes transporting charges and creating the electric potential difference between them.
It uses the triboelectric effect that make two different materials getting charged when they are separated.

Influence machines

In electrostatic influence machines, the charge carrier is a set of conducting material plates insulated from one another.
When two plates are connected (or a plate with the capacitor), the opposing plates induce charges in them creating a movement of charges. When the plates are disconnected, this leaves a difference of charges between the plates.
Charges in plates induce charges in the opposed one when it gets to the electrode.

*Wimshurst machine charge cycle*
Picture source : wikipedia

TESTING A WIMSHURST MACHINE

Wimshurst machine Amazon — *The Wimshurst machine we bought*
Picture source : amazon.fr

This part of our work had two aims :

First, we had to propose a model to describe how the machine works;

And then, we had to quantify the energy available with this generator;

To carry out this study, we bought a Wimshurst machine on Amazon and we tested it.

Because of the way charges are carried in an electrostatic generator, we first proposed to model it by the following electric circuit :

In this case, one has the following relation between the different physical quantities :

`I_0 = I_c = C (d U_c)/(dt)`

Let's assume that `I_0` only depends on `Omega` the angular speed of the machine which in turn does not depend on the time `t`. The following equality is then true if the machine is charged from a completely discharged state after `t=0`:

`U_c(t) = (I_0(Omega))/(C)t`

Then, the time of the first spark will be :

`t^star = (R d C)/(I_0(Omega))`

with `R` the dielectric strength of the air and d the distance between the electrodes.

First model electrical circuit — *Our first electrical model for the generator*

We now needed to find a way to get concrete values for our model. To achieve that, we timed the first sparks for different angular speeds and drew the curve of the time of first spark against the angular speed. We found that as a first approximation, for angular speeds not too close to zero, a linear model seemed adequate. So, we had :

`I_0(Omega) approx a Omega` with `a in RR`

There still remains some work to find a more precise model!

Model value curves — *Results of our first experiment*

We now had a model for the current produced by the generator, but we still missed the value of the capacitor in the machine. We had to find another way to determine its value.
To find this quantity, we decided to mount an electrical resistance in parallel to the capacitor and to measure the voltage across it.
Asymptotically, one has for this circuit :

`I_0(Omega) = I = (U_R)/(R)`

This gave us the second equation to completely determine the practical model of our Wimshurst machine.

Experiment circuit with resistance — *The electrical circuit for our second experiment*

At this moment, we were able to predict the energy output of our generator. The remaining task was to use this energy to ignite our fuel, and so to find a suitable fuel.

SETTING THE FIRE

Minimum Ignition Energy (MIE)

Wikipedia defines the minimum ignition energy as "the minimum electrical energy stored in a capacitor, which, when discharged, is sufficient to ignite the most ignitable mixture of fuel and air under specified test conditions."
This quantity will be very important for us because our capacitor can only store a finite amount of energy. Thus, we have to find a material able to ignite with only the energy contained in the capacitor.

First try : A spark in hard flammable material

We first tried to create a spark in a little amount of flammable material such as coal dust or match heads. This try was unsuccessful because of the very low energy of the sparks.

Second try : A spark in a flammable chemical mixture

We then considered creating a spark in a mixture of simple chemicals (Bronze Age friendly) consisting of sulfur, coal and potassium nitrate (black powder). This method was considered unsafe and therefore abandoned.

Third try : A spark in flammable dust in suspension

Lastly, we considered creating a spark in an enclosed location with flammable dust to trigger a dust explosion. For this try, we chose to try with icing sugar because of the granulometry of the material was at the same time accessible without special means and still probably sufficient to detonate the material.

WHAT DID OUR WORK PRODUCE ?

During our work on this subject, we obtained a better understanding regarding certain questions we had at the beginning of this work :

How do some of the most known electrostatic generators of history work?

How are low energy sparks able to create devastating fire incidents?

How to recreate this phenomenon in a controlled manner?

We also were able to propose models to represent the generator we used. This would be useful to build the lighter the question asked for. We also noted that to set fire to wood is impossible with such a device directly.

What is our answer to the problem?

We would use a spark to detonate a dust explosion which would then ignite a piece of wood.

In all cases, any system that we could produce would be much more complicated than any way of making fire used in ancient times.

WHO ARE WE ?

We are two students of the 2023 promotion of the ENSTA Paris, studying applied mathematics. We worked on this project as parts of our school's team competing in the International Physicists' Tournament.

BIBLIOGRAPHY

Examples of fire and explosion accidents caused by static electricity | ALPTEC News (staticgrounding.cn)

Wikipedia pages for : Van de Graaff generator, Wimshurst machine, Dielectric strength, Dust explosion

Page written by Nicolas HUGOT (ENSTA Paris 2023)

Last updated : 2 may 2022