You Decide
Decision-Making Scenario
You own a small plane (a Piper Archer II) that weighs 2000 pounds. You have finished flight school in San Francisco and have taken a few trips up and down the coast. With each trip you are more at ease with your new flying skills. Each landing seems smoother. Ready for something more adventuresome, you decide to fly with your friends into the high Sierra Nevada Mountains and spend a day ice fishing near Lake Tahoe. Fishing is best in the morning, so you get an early start, taking off from San Francisco around 5:00 am and landing at Lake Tahoe around 6:00 am. The ground temperature at Lake Tahoe is 12o F when you land, and the elevation of Lake Tahoe is over 6000 feet. After a day on the water, you decide to head back to San Francisco for dinner. It's now about 4:00 pm, and the temperature has risen to 32o F. You're about to board your airplane with your friends and your fish when you realize that taking off might be a deadly mistake. With the extra weight of the passengers, fish, fuel and cargo, your plane is 550 pounds heavier than the weight of the empty airplane. Before you start for the runway you'd better check the weather report and your chart. You would need to head north over the lake in hopes of gaining altitude to make sure you clear Martis Peak (a high point just north of Kings Beach on the northern shore of Lake Tahoe) by a safe clearance of at least 3000 feet. How fast of a wind will you have? Is it a headwind or tailwind? Your airplane will have a horizontal groundspeed of 90 mph. Given poor visibility, will your airplane have the climbing power to get you over the peak? Will your airplane even be able to take off from the runway? You must make an important decision that your life will depend on.
Only careful, mathematical reasoning can bring you to a safe conclusion as to whether or not you can fly at this time. What do you do? Should you stay or go? You decide.
Further Background Information:
This problem is multi-faceted. The solution will depend largely on how powerful your plane is. Luckily, your plane comes with piles of charts (below) that explain how it performs in different conditions.
How will you know if you can even get off the runway? The Take-off Performance Chart will help you figure this out. To use this you will need to know the runway length.
How will you be able to tell if your airplane will get over the mountains? You will need to know how high the mountains are and how far away they are. For much of this information, you will need to consult an Aeronautical Chart. This is a map with lots of information useful to pilots. To learn how to read one of these charts, check out the link in the list below.
You will also need to know how quickly your airplane can gain altitude. The Climb Performance Chart will tell you how quickly your airplane will rise given your pressure altitude.
You may need to use the other altitude measurements, such as density altitude. Do you remember what density-altitude is? If not, review the different types of altitude in the Weather Tutorial under "atmosphere." You'll find a density altitude chart below for converting pressure altitude into density altitude.
You will also need to know how long it takes you to reach Martis Peak after you take off. To figure out how far the peak is from the runway, measure the distance on the aeronautical chart using the five-mile scale in the middle of Lake Tahoe. Then, use your airplane's groundspeed to figure out how much time it takes you to get there.
The most difficult aspect of this problem is the fact that as you climb, your altitude increases, so your climb performance decreases. This makes it hard to compute how much you climb in your trip from the runway to the mountains. The easiest way to deal with this difficulty is to take a 'worst-case' approach. This means you would assume that for your entire flight your climb performance is what it would be at the top of the mountains. This is safe, because at lower elevations, your altitude density is less, so your climb performance is actually greater. A more precise way of doing the problem, however, would be to interpolate. This means to break up the climb into different time intervals, say 1 minute or 2 minutes, and see much you climb in each time interval, adjusting your climb performance as your altitude increases.
Finally, you will need to put all this information together to make a safe decision. You can use the "Decision-Making Process" form and the "Student Worksheet/Guide" to help you along.
Below is a list that contains more than enough information needed to make a sound decision. Not every piece of information is pertinent to this problem, so use your time wisely. Click on the item to review the information found there.
When you are done, ask your teacher for the best decisions as reasoned by our expert pilots.
Resource List
Tutorial Links
As always, you will want to draw upon the material from the
tutorials to assist
you in making your decision. You may find the following links to
tutorial pages
especially helpful. These links will take you directly to the
selected tutorial
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