I have a large 54" (1.37 m) diameter cottonwood tree that is 16 feet (5 m) away from where a storm sewer is to be installed. I am sure roots will be cut, but will this tree survive? If the chances are not good, how long would it take to show signs of dying?
Sounds like a very nice tree and worth some consideration. Mark off on the ground where you think your lot line is. Then pace off the distance from the base of the tree to the drip line (extreme-most branches twigs). That gives you the radius of the likely root circle. Now figure what portion of the circle will be affected and express it in percent. Now we have numbers.
Call the local forestry department or works department in charge of the sewer work and tell them about your tree and how it is likely to be affected. The forestry people are really anxious to work with you to minimize the effect on local valuable trees. They have to show due diligence and will appreciate your call. It shows you are interested. Keep a note of your contact efforts.
They will probably send someone to talk to you. Ask them what they can do to minimize the effect on the tree and ask their advice on remedial measures when the roots are removed. Get them to mark exactly where they think the lot line is with fluorescent marker so the guys on the backhoe can see it even through a dirty window. The city has full control over their side. Your roots if any on their side have "escaped" your property. The installation crew may be able to narrow the trench where they go past your tree, minimizing root damage (in particular there are various sizes of digging bucket. They don't have to use a 3 foot bucket to bury a one foot pipe).
16 feet is a nice good distance. Please report back what portion of the root area will be affected. If you need help with calcs just say so. After the work it will be about a year before you see any effect in the tree, since we are going into the fall. Good luck.