Date: 201809
Local time of day: 0601-1200
Location: BTL.Airport, MI
Weather elements / visibility: Rain; 1
Aircraft: Gulfstream II (G1159)
Operator: Personal
Operating under: Part 91
Flight plan: IFR
Mission: Ferry / Re-Positioning
Flight phase: Initial Approach
Airspace: Class D BTL
ATC / advisory: TRACON AZO
Reporter organization: Personal
Reporter function: Pilot Not Flying; Captain
Reporter qualification: Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Multiengine
Human factors: Communication Breakdown; Distraction; Human-Machine Interface; Training / Qualification
Anomaly: Deviation - Altitude Overshoot; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Unstabilized Approach
Detector: Person Flight Crew
When detected: In-flight
Result: Flight Crew Executed Go Around / Missed Approach; Flight Crew Returned To Clearance
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: This was a ferry flight so [I] was using it as training for my low time copilot who was flying from the left seat. He was doing very well as we were vectored in for the ILS 23R at Battle Creek BTL. I let him make the mistake of waiting too long to slow [the] approach speed. Lansing waited to give us a heading to intercept the LOC until we had crossed it AND gave us a bad intercept heading to boot. Of course; this was probably our fault since we were still doing 250kts. The Controller asked us if we could continue and I let the copilot make the decision to do so; knowing we'd go missed and come back in for the RNAV 5L. Just after we were asked to switch over to Tower; a bunch of things happened at the same time at the perfect moment.1. I accidentally punched in the wrong frequency for Tower; and being new to the aircraft myself; once I realized it; I pushed the wrong button and lost Lansing's frequency. Now I had to look down to retrieve and re-enter Tower or Approach.2. We executed the missed; and of course after 3 calls to the Tower; I realize we're on the wrong frequency and had to look down.3. Because of the bad vector; when the Pilot Flying hit the go around button; the FMS didn't auto sequence so he was kind of lost. I was still looking down to get the frequency and he got off track and altitude climbing instinctively as you would do in a missed and he climbed through the set altitude of 3;000 feet. I caught it at 3;800 [feet].From there I checked in with Lansing; gave my copilot a couple quick tips and an altitude and heading call out and everything was fine. There was maybe a minute where we weren't tracking properly; not talking to anyone; AND climbing through the missed approach altitude!My unfamiliarity with a new aircraft type caught me off guard with something as simple as a frequency change at just the right moment. Maybe equipment could be better standardized? I should have made sure I was better prepped. I knew I was a little confused with the audio panel.I could have taught my copilot a better lesson by not accepting the approach since we were so poorly set up. Although; I did want to come back for the RNAV 5L; so at the moment; it seemed fine. I could have asked him to slow down; or asked for a better vector; and certainly would have if it weren't a ferry flight. I think he learned a ton from the event; as did I. ATC apologized for the late and poor vector; but I don't think it was on him at all. I think he may have been taken off guard by our speed. Maybe ATC shouldn't offer the approach at some point because a weaker crew may have continued the bad approach with a descent and a really bad outcome. We accepted the approach but it was my intent to make my copilot go missed anyway and we never even descended; so it worked out well until I screwed up the radios.




Synopsis: Gulfstream G200 Captain reported while giving instruction; a culmination of events resulted in an altitude overshoot and incorrect routing.