“Ladies and Gentlemen due to weight restrictions we are looking for 7 volunteers who have flexible travel plans to volunteer their seats for a later flight.” Words that send shrills down the spines of travelers.
If there are 50 seats on a plane, why can't all 50 be occupied? MLW or Maximum Landing Weight.
To keep it simple I am going to use the following 100% fictitious numbers.
Maximum Takeoff Weight (MTOW)=62000
Max Ramp weight: 62250
Maximum Landing Weight (MLW)=52000
Basic Operating Weight (BOW)=34000
The fuel burn between Boise and Santa Fe (our destination) will be 9200 pounds. The dispatcher planned on burning 250 pounds on the ground during taxi out of Boise. So add those together and you get 9450. Together with the BOW brings us to 43450 pounds. The weather in Santa Fe is ½ mile and overcast 200. Because of this we need a landing alternate. Due to a large low pressure system in the area the closest airport that qualifies that has staffing from our airline is Tuscon. The fuel burn from Santa Fe to Tuscon is planned at 6600 pounds. The weight...before any passengers and cargo is now 50050 pounds. We still need to be able to fly for an additional 45 minutes. That will take 1600 pounds bringing us to 51650 pounds.
Now this time of year the airline thinking the average adult weighs 190 pounds (in summer every passenger is assumed to weight 5 pounds less....reason...no winter coat...both physical and...well fat). Kids are assumed to weight 95 pounds.
On the flight today are 47 adults, 3 kids and 2 infants (infants weigh nothing). Total weight is estimated at 9215 pounds. The cargo weighs in at 1900 pounds. Total weight sitting on the ramp is 62765 pounds. Take away the 250 pounds of fuel that will burned during the taxi out brings us down to 62515 pounds. Five hundred fifteen pounds too much for takeoff. Before we can even depart the gate, 3 adults will have to be left behind. After removing 3 adults ramp weight is now 61945 pounds. But wait....there's a problem....we can't land!
The enroute burn to Santa Fe of 9200 pounds bring us down to 52745. Seven hundred forty five pounds too much. Thus we need to leave more people behind....in our case 3.92 adults..or 4 people.
Taking off 4 adults would reduce the estimated landing weight down to 51985. So our 50 passenger jet can only take along 43 people today.
Aside from leaving seven people behind the airline could leave behind about 1300 pounds of bags. The problem is the airline would have to pay a third party a hefty fee to hand deliver the bags to the customers. The cost has to be weighed (pun intended) too see if it's cheaper to leave behind people or bags. Most of the time people are cheaper.
It's been rumored that some gate agents will count some people as kids...even if they aren't....to get everyone on board. I can't say I have ever seen it.
When we get our computerized weight and balance it list adults and kids. The flight attendant also brings up a passenger count with adults, kids and infants. Most of the time the numbers are close or spot on.
Weight and balance problems can be very complex. If they are done incorrectly they can be deadly.
In 2004 Air Midwest 5481 crashed shortly after takeoff. The weight and balance planning used FAA approved average weights. After the crash it was realized that the plane was actually 600 pounds over MTOW and the center of gravity was too far after as well.
In my two years I have only been on a handful of flights where we had to leave people behind.
Thankfully my plane is a little overpowered and can take a full load. I have been in a MLW situation due to burning significantly less fuel than planned. The solution to such problems is to get help from ATC to fly at a lower altitude if possible. Throwing out drag early also helps. In one situation I had to fly at 8000 feet for the last 45 miles at flaps 20 with the spoilers partially extended in order to get under MLW. Loud...but it worked.
And I was told there would be no math.