What are the channels of interest in your area?Go to this site
http://transition.fcc.gov/mb/engineering/dtvmaps/
and enter Mom's address
tell them your antenna is 30 feet in the air
it'll show you all the stations you're apt to receive
Clicking on one's call letters shows direction to tower and probable strength, more negative means harder to receive
i get two stations just fine that show -50
but not the ones below -70
it also shows the RF channel actually used by the station.
Analog TV was logical but digital TV is not . The channel number identifying a digital station is now just part of its name, not the number assigned to its RF frequency.
When the transition happened many stations kept their call letters and analog channel number but shifted to a new frequency
for example in my neighborhood channel 8, KAIT, is still on RF channel 8
but channel 19, KTEJ, moved to a new frequency, RF channel 20 , when it went digital
and channel 6, KEMV, moved to RF channel 13 and reduced power so much i no longer get it.
The actual frequencies are still in the same old TV bands so there's no need for new antennas but marketeers made a fortune selling "digital antennas" - an absolute hoax.Here are the frequencies that go with RF channel numbers
http://www.csgnetwork.com/tvfreqtable.html
So to recap
i'd use that FCC link to plot out what stations you want to receive
and get an old fashioned antenna that somebody has discarded in favor of a "digital antenna"
and find a direction to point it that works.
Mom's local station should boom in on just a foot of bare wire
so if you make an antenna tune its length for one of your weaker stations at a very different frequency.
I marked up a map to show transmitter locations and wavelengths - half wavelength is good length for a dipole
Since a folded dipole works over nearly an octave , one of them should cover all UHF channels from 14 to 83
Old fashioned classic antennas are log periodic and have great directional behavior
and if all your stations are UHF you could cut the UHF section off an old "analog" antenna for Mom
I've made Yagis for daughter in North Carolina and sister in Oklahoma, tuned them precisely for a weak but desirable station letting the stronger ones just boom in. My sister's simple folded dipole, tuned precisely for Tulsa's PBS, got fifteen stations .
Have some fun at this - and beat the system.!
old jim