Narrative:

I was on an IFR training flight with my student. We departed in piper arrow from ZZZ for montgomery field. Enroute; at ten thousand feet; the flight was challenging with strong headwind and strong downdrafts; having hard time maintaining altitude at times; and some IFR conditions; until we approached julian VOR.about fifteen miles east of julian VOR we experienced severe turbulence and downdrafts completely unable to maintain altitude. At this point we were losing two thousand feet per minute and I decided to make a diversion to the south where there was an opening in the cloud cover and terrain was low. I communicated my distress with the controller who said that there was a cirrus aircraft; which had the same problem and suggested that we turn south and try to approach montgomery via V-66. Quickly we realized that there was no chance for us to cross the mountains as the downdrafts were persisting and the turbulence getting worse.my student was experiencing an anxiety attack and in addition to all other distress he couldn't hold his bladder any longer. I requested to deviate away from the weather toward a VFR airport where we can land and re-group. The controller suggested ZZZ1 airport; so we headed that way and safely landed. I never planned to go that far south and I was not familiar with the airspace; as I would have liked to be.after we refueled and evaluated the weather; the airspace; and our own physical condition we decided to return to ZZZ. As we took off from ZZZ1 we headed for V-66 and westward in order to stay away from restricted airspace and the moas. Since the airspace north of ZZZ1 is completely unfriendly to general aviation; I decided to circumnavigate restricted airspace by flying west and then north. I wish I took V-137; I would have avoided all turbulence; and stayed clear of restricted airspace.as we were in a climb; about five thousand feet; we hit incredible turbulence; like nothing I have experienced ever before. The arrow was everywhere; on one side one second then on the other the next one. I grabbed the controls from the student; so I can keep the aircraft upside right. My student was vomiting in our VFR chart; and I was completely disoriented at this moment; with my attention divided between way too many distractions. When I called for flight following to get some help and stay out of trouble; I was already in restricted airspace. I made a one-eighty turn; but it was too late. Finally I got the vector I desperately needed to continue VFR to ZZZ where the rest of the flight was uneventful.

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Original NASA ASRS Text

Title: PA-28 instructor pilot reported encountering severe turbulence that led to an airspace incursion.

Narrative: I was on an IFR training flight with my student. We departed in Piper Arrow from ZZZ for Montgomery Field. Enroute; at ten thousand feet; the flight was challenging with strong headwind and strong downdrafts; having hard time maintaining altitude at times; and some IFR conditions; until we approached Julian VOR.About fifteen miles east of Julian VOR we experienced severe turbulence and downdrafts completely unable to maintain altitude. At this point we were losing two thousand feet per minute and I decided to make a diversion to the south where there was an opening in the cloud cover and terrain was low. I communicated my distress with the Controller who said that there was a Cirrus aircraft; which had the same problem and suggested that we turn south and try to approach Montgomery via V-66. Quickly we realized that there was no chance for us to cross the mountains as the downdrafts were persisting and the turbulence getting worse.My student was experiencing an anxiety attack and in addition to all other distress he couldn't hold his bladder any longer. I requested to deviate away from the weather toward a VFR airport where we can land and re-group. The Controller suggested ZZZ1 Airport; so we headed that way and safely landed. I never planned to go that far south and I was not familiar with the airspace; as I would have liked to be.After we refueled and evaluated the weather; the airspace; and our own physical condition we decided to return to ZZZ. As we took off from ZZZ1 we headed for V-66 and westward in order to stay away from restricted airspace and the MOAs. Since the airspace north of ZZZ1 is completely unfriendly to general aviation; I decided to circumnavigate restricted airspace by flying west and then north. I wish I took V-137; I would have avoided all turbulence; and stayed clear of restricted airspace.As we were in a climb; about five thousand feet; we hit incredible turbulence; like nothing I have experienced ever before. The Arrow was everywhere; on one side one second then on the other the next one. I grabbed the controls from the student; so I can keep the aircraft upside right. My student was vomiting in our VFR chart; and I was completely disoriented at this moment; with my attention divided between way too many distractions. When I called for flight following to get some help and stay out of trouble; I was already in restricted airspace. I made a one-eighty turn; but it was too late. Finally I got the vector I desperately needed to continue VFR to ZZZ where the rest of the flight was uneventful.

Data retrieved from NASA's ASRS site as of July 2013 and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.