# Math Help - Can the wrong diameter drill bit cause excess Carbon Monoxide?

1. ## Can the wrong diameter drill bit cause excess Carbon Monoxide?

I believe the answer is yes, but I need the math behind it that will prove it. I work in the HVAC industry in Colorado and there is a very large number of houses that are converting from LP gas (in tanks located at residence) to Natural Gas which is being supplied by local gas company. In this conversion process, there is a different size gas nozzle that is available from the manufacturer for each appliance that needs to have this gas conversion. However, there is a common practice up here for an untrained technician to take the existing brass nozzle made for LP gas and use a hand drill and a bit to enlarge the opening. My thoughts are that if the angle of the drill bit is changed while drilling, that the true diameter of the hole will be enlarge. I just don't think a human can precisely drill a perfectly perpendicular hole through a small nozzle while holding the nozzle between his knees. I know most people out there have drilled a hole in something with a drill and bit and sometimes you did not have the right bit and the hole is too small. The easy solution is put the bit back in the hole and simply change the angle of the bit while it is turning. This does ream out a larger hole, but more often than not,, now the whole is too big. Air and gas mixture is very critical in percentages so that the gas is burned completely and does not form carbon monoxide as a by-product of the burn. You cannot adjust the oxygen content of the air in someone's home so that is pretty much a constant. You can adjust the gas going into a burn tube by changing the size of the nozzle delivering the gas. If the hole is bigger than it is suppose to be, then there is more gas than can combine with the available oxygen and this is when it is burned will create carbon monoxide. NOT A GOOD THING!
For example: The new hole needs to be .1990 or the volume of this diameter circle. This is a pretty small diameter bit and this diameter is critical to keep a 10 to 1 Natural Gas to Oxygen mix in our area.
Here is my MATH Question: If the cylinder shaped hole should be H= 1/32 and Diameter= .1990 and this is being done by hand with a .1990 drill bit, what would the resulting area of this OVAL shape be if while drilling, the drill bit was shifted 1 degree, 2 degrees, 3 degrees, 4 degrees and 5 degrees from original perpendicular cylinder? HVAC is an unregulated industry in Colorado and there are a lot of scary things going on up here from the standpoint of supposed HVAC techs taking short cuts or cutting costs that I believe are endangering the customers. I am a trained and nationally certified HVAC tech working in Colorado where no official training or certifications are required. I am trying to put together a white paper for the local gas company so they understand these dangers and possibly mandate that a true replacement kit from a manufacture is better than letting someone into your home to adjust your gas combustion with a hand drill. I am asking assistance in explaining and verifying the geometric changes that can happen to this nozzle if someone does not have a super steady hand.

2. ## Re: Can the wrong diameter drill bit cause excess Carbon Monoxide?

As a rough estimate the area of the ellipse that results from a round drill bit entering at an angle $\theta$ with be a factor of $1/\cos\theta$ times larger than if the drill bit was perfectly perpendicular. So for the values you asked about the amount of excess area is:

1 degree: 0.02%
2 degrees: 0.06%
3 degrees: 0.14%
4 degrees: 0.24%
5 degrees: 0.38%

This assumes that the error is in alignment in one axis only so the resulting hole is an ellipse. If the drill bit is allowed to "wander" in a curcular manner to create a larger diameter round hole then the areas would be larger - up to 0.77% for the 5 degree misalignment.

3. ## Re: Can the wrong diameter drill bit cause excess Carbon Monoxide?

Thanks for your answer, ebaines! Can I use these percentages on any diameter holes? I would assume I would take the diameter and multiply it by the percentage of change and take the results and add it to the original diameter to show the new area. Is this correct?

4. ## Re: Can the wrong diameter drill bit cause excess Carbon Monoxide?

You simply add these percentages to the orinal area. For example: if the nominal diamter is 0.199 inches then the nominal area is $\frac {\pi D^2}{4} = \frac {\pi (0.199)^2} 4 = 0.0311 in^2$. A 5 degree error in the angle of the drill bit woul increase this area by 0.38%, giving a new area of $0.0311 (1+0.0038) = 0.0312 in^2$.

I should point out that the calculations in my earlier post assume the material thickness is very thin. If the material is thick relative to the hole diameter then the error is actually less. It also seems to me that in practice the existing hole for propane would likely act as a drill guide, so that the new larger hole pretty much follows the path of the original. My conclusion from all this is that the error in actual hole size is probably inconsequential.

5. ## Re: Can the wrong diameter drill bit cause excess Carbon Monoxide?

Thanks again, I had thought that the mixture would change more than that. At least now, I will have less to worry about...