what is this about? You're currently a Commercial Pilot with your Multi-Engine Land Rating. You have decided to take your friends on a hiking trip to the mountains and rented a PA34 Seneca. The trip out is uneventful, but an unusual heat wave has rolled in just prior to your departure. There are four of you, each with a suitcase, and you've brought back a few items as souvenirs. Thus, your takeoff weight is just about 4,000lbs. During preflight, you noted the density altitude was almost 6,000 feet. Luckily, you thought ahead and landed at a runway with 8,000 feet of total takeoff distance. While the departure direction has only limited mountains, there are many trees and not many suitable landing areas. As you pre-flight, you see a Cessna 182 take-off with just 2 passengers and, from what you could tell, very little baggage. They struggle to lift off, taking almost 2,800 feet of runway, and can only hold about a 500fpm ascent. They eventually settle at about 1,500 feet AGL and continue on their way. This situation gets you thinking about your single engine climb-out speed. You reference the Airplane Flying Handbook and POH. You recall that your handbook references single engine service ceiling, which requires a 50fpm climb on a single engine, and your single engine absolute ceiling, above which the aircraft wouldn't be able to hold altitude on a single engine (Airplane Flying Handbook, Chapter 13)