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I am trying to solve some problems on converting from LMT (local mean time) to UTC (coordinated universal time) for flight planning purposes and I have some doubts. The problem is the following:

If the LMT in Delhi (LON=85ºE) is 17:45 (5:45 PM), what is the UTC?

First of all, what I've done is converting longitude into time as follows: $$t=85\cdot4=340\hspace{1mm} min=5h\hspace{1mm}40m$$

But then, in order to compute the UTC time, what do I have to do, either adding up this time to the current LMT or subtract it (and what is the reason)?

$$UTC=Delhi(LMT)\pm t$$

I have checked a website that allows you to convert from LMT to UTC (https://savvytime.com/converter/lmt-to-utc-india-delhi) and I've seen the solution is 11:15 PM.

However, if I add or subtract my result, it is not the same as the given in the website. I suspect it is because in India they are using UTC +5:30 and probably these equations do not contemplate that, but I want to know the opinion of the experts anyway.

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    $\begingroup$ UTC time is used by pilots and flight planners to calculate the ETA at the destination airport. This exercise is obtained from an Pilot's Handbook, and in my opinion the question is suitable for this forum, provided that there is no other in which it may fit better (a tag called "time" exists and its description says that is for UTC related question). Furthermore, a lot of people involved in this forum (pilots, aerospace engineers, et cetera) are familiar with this topic and might be able to help. @mins $\endgroup$
    – Airman01
    Apr 2, 2016 at 18:14
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    $\begingroup$ I guess in that case this is not local mean time (which follows the sun and varies each day, up to 30 minutes over the year) but local time (civil time) based on UTC and time zones. $\endgroup$
    – mins
    Apr 2, 2016 at 19:07
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    $\begingroup$ Local Mean Time is not currently in common use in aviation. India Standard Time may have been originally based on the solar local mean time relative to GMT but for the purposes of answering your original question you should use IST, or UTC + 5:30. $\endgroup$
    – Porcupine911
    Apr 2, 2016 at 21:56
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    $\begingroup$ @mins: I just copied the statement of the problem as it is in the book. I think I'm not confusing it because of the answer below. But I know it's confusing because of the Wikipedia article you showed. $\endgroup$
    – Airman01
    Apr 3, 2016 at 7:13
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    $\begingroup$ Why is this question getting downvotes? Do users not understand that this is an aviation subject? $\endgroup$
    – J W
    Apr 3, 2016 at 14:13

2 Answers 2

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You have almost solved the problem yourself. The website you linked to does not help you because, for some reason, it assumes Local Mean Time (LMT) to be equal to UTC. For your problem, LMT needs to be for 85° of East longitude. So, ignore that website and let's move on.

For every degree of longitude, you calculate 4 minutes of difference from UTC. You have already correctly calculated the LMT difference from UTC for 85°E:

First of all, what I've done is converting longitude into time as follows: $$t=85\cdot4=340\hspace{1mm} min=5h\hspace{1mm}40m$$

This leaves you with the question of whether to add or subtract this difference, as you stated:

But then, in order to compute the UTC time, what do I have to do, either adding up this time to the current LMT or subtract it (and what is the reason)?

Let me start with the reason—the explanation of why we want to either add or subtract the difference between LMT and UTC—and then give you the solution.

LMT can be thought of as roughly equivalent to time based on the Sun's position. It is not equivalent to that, which is Solar Time, but it is related. Keeping that approximation in mind, consider the difference in time between when the sun reaches solar noon over Delhi, and when the sun reaches solar noon over London. As the earth rotates, the sun reaches solar noon first over Delhi, and then, a few hours later, over London. Thus you know that UTC will be a few hours behind Delhi LMT. This means that you need to subtract the calculated difference between LMT and UTC.

Another way to put this is: LMT for East longitude is ahead of UTC (subtract the difference to find UTC), and LMT for West longitude is behind UTC (add the difference to find UTC). Thus a more proper way to perform your calculation mathematically would be to properly incorporate the negative sign:

$$t=-85\cdot4=-340\hspace{1mm} min=-5h\hspace{1mm}40m$$

Therefore, if the LMT in Delhi (LON=85°E) is 17:45, then:

$$UTC=12h05m$$

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    $\begingroup$ Perfect! Now I understand everything, I was very confused because of the website but now I see I was not so much lost. So when I said LMT (local mean time) is that correct? Because @mins said I was confusing "local mean time" with "local time", I just copied the statement of the problem right as from the book. Thank you so much for the answer. $\endgroup$
    – Airman01
    Apr 3, 2016 at 7:11
  • $\begingroup$ @Airman01: This is correct, I made a mistake reading the definitions. LMT = civil time. Jonathan has a clear explanation on that. An article about time in maritime navigation that also talks about the difference. $\endgroup$
    – mins
    Apr 3, 2016 at 11:59
  • $\begingroup$ Actually, that is NOT correct. LMT is related to the solar position at a longitude, and is what the answer here gives. Local time is based on politics and includes thing like daylight saving time, etc. One cannot figure out local time from a formula alone. You must know the offset from UTC (including any DST rules) in effect for the date and time being converted. This is decided by governments, not by math. Computers use the tz database for this. $\endgroup$
    – Matt Johnson-Pint
    Jul 24, 2017 at 18:17
  • $\begingroup$ @MattJohnson I fail to understand what you are referring to as "NOT correct". The information you offer above seems to affirm both my answer as well as the other comments on this question. What do you intend to address by your comment here? $\endgroup$
    – J W
    Jul 24, 2017 at 18:26
  • $\begingroup$ The part in the second comment here (by @mins) that says "LMT = civil time". Civil time is local time, as used by people on the ground, which is controlled by governments. LMT is the longitudinal time that you correctly describe in your answer. $\endgroup$
    – Matt Johnson-Pint
    Jul 24, 2017 at 18:28
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Use this simple Formula:-

For places with East Longitude LMT = UTC + dLong/15

For Places with West Longitude LMT = UTC - dLong/15

(Where dLong = Distance between the two Longitudes)

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