Narrative:

There was aircraft X transitioning from south to north at 077. Before I cleared aircraft Y for takeoff; I told him the position; altitude and intention of aircraft X. When he tagged up; I called the traffic again; he didn't have him in sight. I turned aircraft X 20 degrees left; thinking that would be enough.the traffic started to build so the controller in charge insisted on opening local control-2. Since aircraft Y still did not have aircraft X in sight; I told him to remain my frequency; so I didn't send him the departure with a conflict. The controller in charge got in my ear and insisted on the briefing in that moment since the traffic was building. As I was giving the briefing; aircraft Y was at 080; his clearance limit; while aircraft X was still at 077. He told me he was responding to an RA and climbing through his limit.in hindsight I should have turned aircraft X more drastically to get him out of the way. We've had fires in the local area; so although the weather was 'clear;' the sky was filled with smoke; impeding his view.fatigue. We are very short staffed as it is; and have 3 people out for medical reasons; and one out on bid leave.we are still working with too few people in the cab; when we're already so fatigued. The fatigue in this facility is growing exponentially. Our mou states we need X cpcs per day. We really need X+1; but with our staffing number of X+3; we couldn't accomplish X+1 per day even when we're 100% staffed.

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Original NASA ASRS Text

Title: Tower Controller reported an airborne conflict and cited fatigue from being understaffed as contributing factor.

Narrative: There was Aircraft X transitioning from south to north at 077. Before I cleared Aircraft Y for takeoff; I told him the position; altitude and intention of Aircraft X. When he tagged up; I called the traffic again; he didn't have him in sight. I turned Aircraft X 20 degrees left; thinking that would be enough.The traffic started to build so the CIC insisted on opening LC-2. Since Aircraft Y still did not have Aircraft X in sight; I told him to remain my frequency; so I didn't send him the departure with a conflict. The CIC got in my ear and insisted on the briefing in that moment since the traffic was building. As I was giving the briefing; Aircraft Y was at 080; his clearance limit; while Aircraft X was still at 077. He told me he was responding to an RA and climbing through his limit.In hindsight I should have turned Aircraft X more drastically to get him out of the way. We've had fires in the local area; so although the weather was 'clear;' the sky was filled with smoke; impeding his view.Fatigue. We are very short staffed as it is; and have 3 people out for medical reasons; and one out on bid leave.We are still working with too few people in the cab; when we're already so fatigued. The fatigue in this facility is growing exponentially. Our MOU states we need X CPCs per day. We really need X+1; but with our staffing number of X+3; we couldn't accomplish X+1 per day even when we're 100% staffed.

Data retrieved from NASA's ASRS site 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.