Bowl Size And Smoking Duration

[Professor Moriarty]

Time required to smoke a bowl of tobacco depends only on the depth of the bowl.

PROOF
Consider a bowl of volume V , depth d, and radius r (radius = 1/2 inner diameter) in mm.
V determines how many cubic mm of tobacco the bowl holds when completely filled.

t is the duration of the bowl in minutes (time elapsed from smoking the bowl from top to bottom).

Approximate the shape of the chamber as a cylinder so that V = d*pi*r**2
(Consider the "dish" at the bottom to be unsmoked dottle)

Assertion: combustion rate C of the tobacco is proportional to surface area of exposed tobacco (pi*r**2).

C = f*pi*r**2, where f is a constant measured in mm/minute and depends on tobacco, packing, puffing, smoking conditions, etc.

duration is proportional to volume and inversely proportional to rate of combustion:
t = V/C = d*pi*r**2 / f*pi*r**2 = d/f
Q.E.D.

THEORY OF RELATIVITY
Consider two pipes of different size, one with depth d and the other with depth d':

t =d/f and t' =d'/f
t/t' = d/d'
t = t'(d/d')
Duration is proportional to the ratio of the depths, regardless of radii!

Example
If a certain pipe lasts you 30 minutes, and you wish to know how long it will take to smoke one of your larger bowls (with the same tobacco, packing, puffing, and smoking conditions) simply measure the depths of both pipes, ratio the larger to the smaller and multiply by 30 minutes. This also works going from large bowl to small.

And to beat you knuckleheads to the punch: yes, I know, pie are round.

 

[BingBong]

There must be a multiplier between ribbon cut and folded flake.

 

[Professor Moriarty]

There must be a multiplier between ribbon cut and folded flake.

All such considerations are held in the combustion constant, f

 

[VDL_Piper]

You need a whole new set of calculus for Samuel Gawith flakes…………….

 

[Chasing Embers]

You called the chamber a bowl. Theory debunked.

 

[Professor Moriarty]

Calculate your f as d/t, bowl depth divided by time to smoke that bowl. It is a measure of how fast you smoke.
The slower you smoke, the smaller your f. For the blend I am currently smoking, McClelland #8, my f is 33mm/90min = 0.37 mm/minute.

 

[rectifythis]

.....I was told there would be no math....

 

[Professor Moriarty]

You called the chamber a bowl. Theory debunked.

From my initial post -- "Approximate the shape of the CHAMBER as a cylinder"
I am aware of the difference, and though I do interchange "bowl" and "chamber", I did my best throughout the post to be clear in context. One does not measure the DEPTH of a bowl. The bowl is properly measured as HEIGHT. People usually say, "I'd like to try this tobacco in a bigger bowl." when of course they mean "chamber".

 

[VDL_Piper]

What about if you’re trying to smoke cube cut St James Plug in the Main Street of Leadville Colorado Vs the same smoke in Phoenix Arizona?

HRR = Heat Release Rate
Lower oxygen content and ambient pressure reduce the HRR; for example, the HRR at an altitude of 4150 m is nearly half at an altitude of 500 m, contributing to a lower smoke release rate. The HRR is proportional to 1.3 power of atmospheric pressure, and a fitting equation was brought out in this paper. Flame height increases with the increase in altitude due to the demand for more oxygen during the combustion process since the oxygen content is low in high-altitude areas.

The burning rate is predicted to increase by 9.4 % for every 50 °C increase in ambient temperature. The core diameter was found to have a slightly larger impact on the burning rate than the wall thickness. The effect of using different wall thickness materials was evaluated and indicated that the burning rate is significantly influenced by the wall material when the thermal conductivity is increased and the volumetric heat capacity is reduced. The shape of the combustion front was found to widen with a long tail for materials with a low thermal conductivity and a narrower combustion front with a short tail for materials with high thermal conductivity.

You have a lot of variables not considered in your hypothesis

 

[bullet08]

I don't know. Majority of my pipes, regardless of the bowl depth, finish around an hour and half.

 

[OzPiper]

You also need to factor in what you are doing while smoking.

A bowl could last several hours if I’m watching cricket - allow for a snooze during slow overs eg if Geoff Boycott was batting

 

[Professor Moriarty]

I don't know. Majority of my pipes, regardless of the bowl depth, finish around an hour and half.

Actually, this is what inspired me to do the analysis. My small and medium size bowls all last about 90 minutes with most blends. Although large bowls last about 120 mins.
I am curious to understand why a small bowl lasts as long as a medium bowl.
Interesting that you have the same experience.

It seems a waste to burn more tobacco in a larger bowl for the same 90 minutes of pleasure.
My hypothesis is: a large diameter chamber burns tobacco faster than a small one, thus negating its larger volume.
The math bears this out--and it is true that if I fill a bowl 3/4 full, it will last only 3/4 as long.

Maybe the theory applies better to fast smokers, or very large pipes, or maybe we need to measure depth and time more precisely.

 

[bullet08]

Actually, this is what inspired me to do the analysis. My small and medium size bowls all last about 90 minutes with most blends. Although large bowls last about 120 mins.
I am curious to understand why a small bowl lasts as long as a medium bowl.
Interesting that you have the same experience.

It seems a waste to burn more tobacco in a larger bowl for the same 90 minutes of pleasure.
My hypothesis is: a large diameter chamber burns tobacco faster than a small one, thus negating its larger volume.
The math bears this out--and it is true that if I fill a bowl 3/4 full, it will last only 3/4 as long.

Maybe the theory applies better to fast smokers, or very large pipes, or maybe we need to measure depth and time more precisely.

That makes sense in theory. But in practice, almost always, center will burn down quicker. This leads to redistributing the tobacco and relight, sooner or later.

I always try for even coverage of the top when I lit the tobacco, but never seen it burning down evenly. Probably had to do with single point of exit in the bowl.

 

[Professor Moriarty]

That makes sense in theory. But in practice, almost always, center will burn down quicker. This leads to redistributing the tobacco and relight, sooner or later.

I always try for even coverage of the top when I lit the tobacco, but never seen it burning down evenly. Probably had to do with single point of exit in the bowl.

Physicists call this an "edge effect".
Nevertheless, the "center burning circle" which you observe is still larger in a larger diameter chamber.

I have a few pug shaped bowls with high radius/depth ratio. These pipes yield only a brief smoke. Same with Prince shaped bowls.

 

[hoosierpipeguy]

My math says it takes as long to smoke a bowl of tobacco as it takes for me to enjoy it. There are numerous variables your may fails to account for. Modo, smoking technique, tobacco type and many more. I'm an certain I do not want to consider math while I'm smoking a bowl of tobacco.

 

[georged]

And to beat you knuckleheads to the punch: yes, I know, pie are round.

Punch ducked, counter right uppercut to the solar plexus delivered:

 

[HeavyLeadBelly]

Dear lord I thought my brain was already broken but this broke it even more

 

[dog_park_piper]

Will this be in the test?

 

[dog_park_piper]

Yes, I’m moving toward smaller diameters and deeper chambers.

 

[Roach1]

Too complicated for me. How long the bowl lasts is relative for me.