General aviation instructor pilot reported a low altitude event while on a training flight during student training maneuvers. The instructor took control of the aircraft during a maneuver to remain clear of a congested area and an unmarked tower obstacle; then transferred control back to the student.

Narrative

I was instructing a commercial pilot applicant at around XA:30 in the afternoon. Clear day; winds gusting from the south at about 20 knots. We took off with 15 knot winds. Turbulent below 4000 feet MSL. Since the student pilot was near a checkride; I; as the instructor; was doing a 'mock' checkride and was evaluating the student. I was not manipulating the flight controls. First; after taking off from MDH; we climbed to 4;500 MSL to do our at altitude maneuvers. After these were completed; the student and I descended down to pivotal altitude. I as the IP (instructor pilot); remarked to myself that we were close to a town and wanted to see what the SP (student pilot) would do. The student pilot picked his first pylon about a mile and a half south of this town. Our ground tract took us just south of the town; away from flying over a congested area (we were above 1000 AGL). It was about a quarter through the turn that I noticed an unmarked tower near our point. I called this out to the student pilot and he said that he had it in sight. It was no factor through our first complete turn. I then turned my attention to his altitude; airspeed; and coordination; trying to evaluate his maneuver. For reference; the ground level was about 500 feet above sea level. During the second half of the turn; with strong 15-20 knot winds (resulting in a high variance of pivotal altitude); Aircraft X was about to descend past 500 feet AGL in order to maintain pivotal altitude; but as IP (Flight Instructor); I stopped him from doing so. After reaching the completion of the Eights On Pylon maneuver; I asked the student if he wanted to try the Eights on Pylons again. Looking back on the question; I should have prefaced the question with my intention of moving away from the town and unmarked tower. I did not want my student to try Eights on Pylons again being close to a congested area and a tower we were not familiar with. My student said yes to a retry and immediately turned left to start again; this time about 200 feet lower. With us being so close to the congested area; I immediately started a climb while we were in the bank to the left. At this point; I had momentarily forgot about the unmarked tower. The unmarked tower has no marked altitude height; but I can estimate that we climbed just west to the tower about 1000-1250 feet; and 800-1000 feet vertical clearance. While there was no collision imminent; the decision to turn left resulted in a loss of adequate separation with the tower. We climbed to 1700 feet MSL and proceeded farther southwest to continue our practice of Eights on Pylons. Here; the ground elevation rose about 30-50 feet; and neither I nor the student pilot realized it. We; without realizing; accidentally descended below 500 AGL with this new rise in field elevation; about 30-50 feet. I checked the field elevation during the maneuver; and I realized this during the maneuver. Since we were on the climbing part of the maneuver; I allowed the student to finish after climbing back to 500 AGL; and went back to the airport to land without incident. Looking back; I made several errors.1. I should have forced the student to pick a different area. While his initial point was legal; it should not have been so close to a congested area.2. I lost situational awareness due to my monitoring of the student's maneuver. I needed to make decisions as PIC and not as a flight instructor.3. While flight instruction is important and trying to evaluate the student's performance is needed at times; the PIC must take control of the situation and not let students make a choice not conducive to safety of flight.In the future:1. I will be enforcing a 3 mile no-fly radius around congested areas for ground reference maneuvers.2. I will not allow flight instruction to overshadow my duties as PIC.3. Make sure to double check the field elevation in the area before starting Eights on Pylons.