How to calculate airplane noise as a function of distance?

[sophiecentaur]

I believe that Alexander Graham Bell found that a sound appears half as loud when it is one tenth the power. This is one Bel or 10 decibels. So a 10dB reduction will sound half as loud.
By increasing the distance about three times, the aeroplane will sound half as loud.

But not half as annoying.

 

[Wes Turner]

Where did you get that formula for calculating dB? You may have read someone’s workaround for a particular case but why not use the formula with log base ten?
look at Wiki for all you need to know about deciBels and for the right formula.

The way I get pretty much everything -- by the seat of my pants.

I looked at a bunch of websites, including Wikipedia. I was too lazy to go through all of the math and physics having to do with pressure vs voltage vs who knows what. But the phrase that I read over and over, including here, was that you double the distance and you lose 6 dB. It was pretty easy to come up with my formula from that:

What I didn't realize, and what most of those sites failed to make clear (not Wikipedia) was that it was approximately 6 dB.

I am surprised that someone like you who rails against those who confuse 3 times larger and 3 times as large, one of my minor pet peeves, would not point out that it is only approximately -6 dB.

I have fixed my table. It now looks like this:

I’m not being difficult or elitist here.

Not at all. I have no problem with you pointing out errors in my math or my logic. I appreciate it. And the tone doesn't much matter to me as long as the commentary is correct.

 

[Wes Turner]

dB₁ = dB₀ - 6.0206 * Log₂( D₀ / D₁ )
Now change the base from 2 to 10.
dB₁ = dB₀ - 20 * Log₁₀( D₀ / D₁ )

Thanks for that correction. I have now found that equation on several websites as well. And I just posted my corrected table.

Thanks

 

[Wes Turner]

Your tables would be handy for getting a rough idea of how distance and height is likely to affect what you hear but, the angle changes a lot (reducing as the plane goes further away) so it would be risky to quote those values in a dispute because they are very approximate and could affect your credibility. If more detailed evidence is available then that's what you should quote publicly.

I think this is the key point -- or two points really.

First, I really don't care whether the sound is louder as the aircraft is approaching, directly overhead, or going away. I only care about how loud it is at its loudest point. And unless that is a significant distance from directly overhead so that the line-of-sight distance is significantly greater, it doesn't matter. In addition, the aircraft are on a glide path -- that is, descending. So that will offset at least some of the increase in the distance after it has passed by. And finally, the sound monitors that they have placed in three spots around the city are recording the maximum volume, which is all that the neighbors care about. But unless they are close to your house, the sound you hear would be different.

Second, and this is more important, several comments on the websites and here suggest that the human perception of volume is subjective on several levels, so any instrument reading may not be a perfect measure of what one person or another would perceive.

In short, all I am trying to do is provide a way to measure the relative impact of increasing the elevation of the glide path, moving it farther away, or some combination of both. I argue that whatever the limitations of the numbers in my tables, they can do that job. And in fact, I argue that the percentage table is probably the best at that task. I have heard no complaints about incorrect equations there. It makes it quite clear that moving the glide path 0.75 miles away has the same effect (~50% reduction in volume) as raising the flight path by 1,600', something that the guy from the airport seemed to say was highly unlikely. Furthermore, raising the glide path by the recommended 1,100' and moving it 0.75 miles away will reduce the volume by over 60%.

Do you take issue with any of that?

 

[Wes Turner]

I believe that Alexander Graham Bell found that a sound appears half as loud when it is one tenth the power. This is one Bel or 10 decibels. So a 10dB reduction will sound half as loud.
By increasing the distance about three times, the aeroplane will sound half as loud.

This gets to my second point above to Sophie. Are you saying (or are you saying that Bell said or observed) that while doubling the distance reduces the power to 25%, not only is that not perceived as 25% as loud by people, but it has to get down to 10%, which means increasing the distance by a factor of ~3.16 (10^.5)?

 

[Baluncore]

Furthermore, raising the glide path by the recommended 1,100' and moving it 0.75 miles away will reduce the volume by over 60%.

Ideally, the glide path will be lined up exactly with the runway so the pilots can land safely at the end of a long delayed flight.
Jet aircraft are slippery and take some stopping. A steep descent means they will generate more aerodynamic noise creating turbulence to waste the excess kinetic and potential energy. A shallow descent will require continuous engine power. Maybe you can find out what the minimum noise glide slope angle is for the noisy aircraft that land most often.

 

[sophiecentaur]

Do you take issue with any of that?

One or two issues:
The heights of aircraft approaching and leaving an airport are chosen for good reasons - safety and economy. You can't expect an individual aircraft to deviate much from its 'usual path' without good reason. My story, above, about aircraft climbing rapidly from Heathrow, so that they were higher by the time they reached the airport perimeter, is an example of possible action. I don't think they do it any more.

The figures in the tables imply that there is some trade off between close and high or low and distant, which there isn't really. @Baluncore points this all out in more detail. Lowering the glide path will affect more people, albeit with quieter running engines. That's great for the politicians and developers because it divides and conquers the local protestors.

I'm surprised that you are surprised about the 'magic' value of 6dB not being what you would call accurate. During your reading around, did you not just use your calculator to find out what log₁₀ (0.25) is? 6dB is just an Engineer's rule of thumb and would never be used in a chain of calculations because (obviously) the error would propagate. But the error in the procedure that yielded the original 25% figure far outweighs any second order errors in quoting 6dB.

I have said nothing about the subjective effect of anything. Any results from Bell represent another step in the study and would need to be interpreted very much on the basis of the particular sound and the state of the minds of the listeners. This subject is highly political. It amazes me that new houses are built right next to motorways with 24/7 heavy traffic passing. The choice of new owners, to live there is based on a whole set of circumstances. The cost benefit assessment they make in their heads works on a different set of costs and benefits.

I sympathise about the noise levels around airports but most people who live there moved in long after the age of the Jet aircraft and early morning charter flights (choices choices). At least we can say that modern jet engines are a lot quieter than the earlier ones (VC10, 707 etc). Hopefully (imo) there will be fewer flights in the future. The Air Transport industry may take a hit - but so did the Wool and Flax industries. Choices choices again.

 

[Wes Turner]

Ideally, the glide path will be lined up exactly with the runway so the pilots can land safely at the end of a long delayed flight.
Jet aircraft are slippery and take some stopping. A steep descent means they will generate more aerodynamic noise creating turbulence to waste the excess kinetic and potential energy. A shallow descent will require continuous engine power. Maybe you can find out what the minimum noise glide slope angle is for the noisy aircraft that land most often.

That's what I thought before I attended the community meeting. The point of the meeting was to discuss the insytallation of GBAS (Ground Based Augmentation System), which allows much more precise control of the glide path. They discussed being able to adjust the glide path both vertically and horizontally. They were the ones who talked about elevating the glide path by 1,100' and/or relocating it by up to a mile or so.

Based on the comments I heard, it seemed like people were struggling to understand the options. My objective here is to provide the community with some tools to assess the impact of any changes. I don't think anyone is under any impression that this can be calculated to 10 decimal points of accuracy.

 

[Wes Turner]

One or two issues: . . .

I understand all that and I appreciate the perspective. But I would also appreciate some credit for attempting to provide my community with some tools to assess the plans. Everything I have said about the options were discussed and proposed by the experts at the meeting. I am not suggesting that the aircraft come in at a 45° descent angle or make a 90° turn at the last minute. Yes it's political, subjective, and complex, but that is no reason not to have some analytical tools. And I always planned to include the appriopriate caveats, even though I know some people & politicians will ignore them and/or misuse the information.

 

[Baluncore]

They were the ones who talked about elevating the glide path by 1,100' and/or relocating it by up to a mile or so.

Without the distance from the threshold being specified, absolute offsets are meaningless. It would be a pity if an aircraft landed 1,100' above the ground, or a mile off track.

 

[Wes Turner]

Without the distance from the threshold being specified, absolute offsets are meaningless. It would be a pity if an aircraft landed 1,100' above the ground, or a mile off track.

Now you are just being childish. I'm pretty sure the people leading that meeting knew exactly where the airport is and all of the parameters for a safe landing. Safety was discussed multiple times. The purpose of my table, as I have said many times, is just to give the community some mechanism for evaluating alternatives and possibly offering counter-proposals. But, of course, I think you knew that.

 

[Baluncore]

Now you are just being childish.

No, just obtuse, in response to a lack of information.
So where then is the 1,100' or 1 mile specified ?

 

[Wes Turner]

No, just obtuse, in response to a lack of information.
So where then is the 1,100' or 1 mile specified ?

Jeez, man. I've said several times that the city scheduled a town hall meeting with representatives from the airport and FAA to discuss the installation of the GBAS and how it might enable the airport to make changes to the glide paths. They said that the current glide path puts the aircraft about 4,000' above and pretty much directly over our neighborhood. They also said that they think they can increase the elevation by about 1,100' and possibly move it a mile or so to the east, that would put it over a large body of water.

Sometimes I feel like I'm talking to myself.

 

[Baluncore]

They said that the current glide path puts the aircraft about 4,000' above and pretty much directly over our neighborhood. They also said that they think they can increase the elevation by about 1,100' and possibly move it a mile or so to the east, that would put it over a large body of water.

Sometimes I feel like I'm talking to myself.

Maybe you were. I am sorry, but I did not get that information in earlier posts, maybe it is there, hidden between your voluminous tables.

 

[sophiecentaur]

@Wes Turner . As I see it, you run the risk of having your easily readable table being read by a lot of non-technical residents and being interpreted in all sorts of ways. Don't forget we already had some difficulty in establishing just what those tables should show.

At any public meeting with probably highly paid experts on the 'other side', inconclusive evidence that's been produced on the basis of a flawed algorithm would so easily be turned against your interests. By giving that information to other residents, you could be shooting yourself in the foot. Your attempted justification to me (a disinterested party) didn't really hold water and you could be 'trussed up like a Turkey' by a smart talking expert. The noise nuisance is not just a function of A-B distance, as you have been told several times and that will instantly be pointed out to the meeting.

 

[Wes Turner]

I believe that Alexander Graham Bell found that a sound appears half as loud when it is one tenth the power. This is one Bel or 10 decibels. So a 10dB reduction will sound half as loud.
By increasing the distance about three times, the aeroplane will sound half as loud.

This is interesting. Yesterday, I came up with this equation that calculates the perceived sound as a function of distance.

It appears to work as illustrated by this table, which calculates the percentage of the perceived sound at D₀ that is perceived at D₁:

The distance at H23 is sqrt(10) and the percentge is, at predicted, 50%. The distance at L23 is 10 and the percentage is, as predicted, 25%.

But I can't remember how I got to that formula.

Can you tell me if it is correct and, if so, the derivation?

Thanks

PS: That table only shows the distance in one dimension. I didn't want to burden any of you with my "voluminous" tables.

 

[Wes Turner]

I used the formula above to add a third table.

The top table (rows 6-9) show the percent reduction is sound pressure (power?) as a function of distance. The middle table shows that same change units of decibels. The bottom table shows the percent reduction in the perceived sound volume according the the formula above based on Bell's observation that it takes a reduction in sound pressure to have a 50% reduction in the perceived volume.

Rows 7, 15, & 24 all contain the the same values representing D₁. The distance in Column D is sqrt(2), at which point the sound pressure is reduced by half. The distance in Column E is 2.00, at which point the sound pressure is reduced to 25%. The distance in Column F is sqrt(10), at which point the sound pressure is reduced to 10% and the sound pressure is reduced to 10% and the perceived sound volume is reduced by half. The distance in Column I is 10, at which point the perceived sound volume is reducved to 25%.

Any comments on this? Is it accurate (at least to a first approximation)?

 

[sophiecentaur]

Any comments on this?

Only my previous comment about trying to make the whole thing rest on a very simple model of an omnidirectional source in free space, neither of which you've got with an aircraft. I'd go along with it , fine but an 'expert' could inject a damaging amount of doubt into the validity of those figures. Could involve shooting yourself in the foot.

 

[Wes Turner]

Only my previous comment about trying to make the whole thing rest on a very simple model of an omnidirectional source in free space, neither of which you've got with an aircraft. I'd go along with it , fine but an 'expert' could inject a damaging amount of doubt into the validity of those figures. Could involve shooting yourself in the foot.

As I replied to you last time, I don't have a "foot" in this fight to get shot in -- by me or anyone else. I am just trying to provide the best tool for estimating the distance required to achieve some desired level of backyard quiet. I know it's not perfect and my neighbors know that also. I don't think we have to keep beating that horse.

In short, my central question, now, is this: Is Table 3 above based on the comment from tech99 about Graham Bell's observations the "best" estimate of the "perceived" sound volume as a function of distance? Notice that I put both "best" and "perceived" in quotes so as not to get your knickers in a twist over it not being perfect.

If not, is there a better way to get that estimate that does not entail connecting the plane to the ground with a giant measuring tape and placing drones every meter along that tape to measure temperature, humidity, particulates, ambient noise, wind direction, and the gravitational pull from Pluto?

Thanks

 

[sophiecentaur]

I am just trying to provide the best tool for estimating the distance required to achieve some desired level of backyard quiet.

In what way is the the "best tool"? If it were anything like as simple as the basic inverse square law then it would all be sorted and there would be no argument. What you have done is little better than saying further away and higher is probably quieter. How much quieter is not revealed with such a simple formula. It also doesn't bring in the factor of the number of people who would be affected by any changes in flight paths. What counts is the result of past planning decisions, elsewhere. you need to see just what has or hasn't been allowed and then push to get a decision as much in your favour as possible.

not to get your knickers in a twist over it not being perfect.

Sorry but that's a straw man argument.
They are not in a twist about lack of perfection; they are in a twist because you are insisting that your school-level calculations are the best you can do in a fight against big boys who are willing to spend what it takes to get their way.

I realize that you have a lot invested in your tables but you should see them for what they are and be prepared to consider another approach. You have learned a lot about the general trend of things with your calculations but you really should avoid trying to use those figures in any argument against your opponents.

I suggest calling on paid consultants and that would involve a lot of effort to crowd fund your case. Could well be worth it in the long run.