Here are some requirements, limitations, and notes associated with this program:

• All ships (Sloops, Frigates, and War Galleons) all travel at the same speed, so this program cannot be used to determine the type of an incoming naval attack.
• Though in certain cases it can still be minimally helpful, for the most part this system requires that you have enough Lookout Towers in the city that's under attack that it can see the incoming attack the moment it leaves the attacking city.
• All land-based troops can have their movement speed upgraded using purified food (Trueseed) Research up to a maximum of +50% movement speed. The increments are: 1%, 3%, 6%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, and 50%.
• Movement speed for Barons can be further upgraded to a maximum of 50% (stacks with Research for a maximum possible total of +100%) by the owner's alliance having Palaces to the Spirituality Virtue/Shrine.
• Movement speed for all other land-based unit types can be upgraded to a maximum of +50% (stacks with Research for a maximum possible total of +100%) by the owner's alliance having Palaces to the Compassion Virtue/Shrine.
• You can open the Rankings window and check the Lord of Ultima tab to see whether or not the attacking alliance controls any palaces to these virtues to help in determining attack type
• Apparently all land based troops, siege engines, and trading carts are equipped with personal flotation devices, as they always move from their source to their destination in a straight line, even if that straight line takes them across water. That means that this Calculator works for all land-based attacks on the same continent even if a straight line between the two cities passes through water.
  As an example, troops sent between the two points illustrated in the following World View screenshot travel in a straight line (across the bay) rather than pathing around the shore:
  
• Mixed armies move at the slowest unit type's speed. So an attack of Scouts sent along with even a single Siege Engine will move at Siege Engine speed.
• The Attack Speed Calculator can also be used to calculate the distance between two points in LoU by just entering in both sets of coordinates without entering in any attack time information.
• If an attack was spotted at, say 22:45:00 today and arrives at 01:30:00 tomorrow, just enter those numbers for the times. The calculator adds 24 hours to the arrival time if it's less than the time the attack was spotted.
  Note that this means that the Calculator currently assumes that no land-based attacks take more than 24 hours. That is a bad assumption as Barons and even Siege Engines can take more than 24 hours if they're travelling from one corner of a continent to another. As a workaround, you can manually add 24 hours to the arrival time for every full day between the departure and arrival of the attack.

Instructions:

You must fill in four pieces of information in order to calculate the movement speed of an incoming attack. They are numbered as follows:

1. Click on the Incoming Attacks label at the top of your scren (this trick works whether it's you or an alliance mate getting attacked):
   

2. Of the four pieces of information that you need to enter into the calculator, the second, third, and fourth are all displayed right in the Incoming Attacks window. They are labeled in the following screenshot. You have to click on the name of the attacking city to get the first piece of information.
   

3. When you click on the attacking city's name in the Incoming Attacks window you'll see information similar to the following. You want to copy the coordinates of the attacking city into the first pair of blanks in the Calculator:
   

4. When you are done entering all four pieces of information, simply tab or click away from the last input box you type in to see the calculated results, similar to the following:
   

Interpreting the Results:

In the screenshot above, notice that Baron, Siege Engine, and Infantry are all listed in grey. That is because it's impossible that this attack could be any of those options. Remember that +100% movement speed is the absolute maximum possible, which would require a full +50% Research bonus plus a full +50% Palace Virtue bonus. In the example above, if the attack were Infantry, they would be moving at +164.9% speed, which is impossibly high.

The attack could therefore only be one of two types - Cavalry or Scouts. If it was Cavalry, they would be moving at +32.5% movement speed. This exact number is impossible to achieve by Research alone (it'd have to be either 30% or 35% exactly), though I believe it is theoretically possible with Research and Compassion Virtue bonuses combined. In this case, a check of the Rankings -> Lord of Ultima tab indicates that the attacking alliance has no Compassion Palaces, so therefore this attack cannot be Cavalry.

We know from ruling out all other options that this attack must be Scouts, and that those Scouts have +6% movement speed (which is a valid Research option).

Consider this second example:

Movement speeds can never be negative, so Cavalry and Scouts alone are absolutely ruled out (though Cav and/or Scouts attacking alongside Infantry is possible). Movement speed can never exceed +100%, so Baron is conclusively ruled out. That leaves only Siege Engines and Infantry as possibilities.

If this attack was Siege Engines, they'd have to be moving at +59% speed. That'd require a combination of Research and Virtue bonuses. As in the first example above, I know from the Rankings -> Lord of Ultima tab that the attacking alliance has no Virtue bonuses, making me confident that this cannot possibly be a Siege Engine attack. Later in the game when higher levels of Research and Palace Virtue bonuses are common, it will become more possible that troops could be moving at greater than +50% movement speeds, but at the point we're at on our current World, it's highly unlikely. So any movement speeds in excess of +50% are greyed out in the Calculator.

Therefore, we know that this attack is Infantry, and that it's +6% movement speed Infantry (which is a valid Research option).